BERKELEY 

LIBRARY 


11 


The  Cpticai  Journal  &  Revie'V? 
LIBRARY 


OCULAR     REFRACTION 

AND       THE 

SHADOW    TEST 


FREDERICK     A.     BATES 

NEW        YORK 


With    i4j     Original    Illustrations 


NEW      YORK 

Frederick    Boger     Pub.     Co. 
■\b     .maiden     lane 


The  Optica!  Jo^.arnaI  Sz  Review 
LIBRARY 


r 


OPTOMETM  UBRAM 


Copyright     1903 
by 
UCK    BoGEK   Publishing   Co. 


PRESS      OF 

Jibe  Optical  Journal 


OPIOMETHr 


PREFACE 


This  book  is  dedicated  to  the  advancement  of  the  science  of  optom- 
etry, and  to  those  willing  workers  in  the  field  who  are  ambitious  for  its 
advancement  and  who  are  laboring  to  that  end. 

The  correction  of  errors  of  refraction  of  the  e^e  with  lenses  is  a  noble 
work,  involving  the  betterment  of  conditions  under  which  mankind  is 
enabled  to  enjoy  the  most  valuable  of  the  five  senses,  viz.,  sight. 

Without  glasses  many  would  never  know  the  beauties  of  our  world, 
while  others  would  suffer  ceaseless  misery. 

The  resources  of  optical  science  have  been  greatly  improved,  its  prac- 
titioners have  acquired  more  knowledge  and  skill,  and  its  value  is  becom- 
ing more  appreciated. 

The  limit  of  the  possibilities  of  the  work  have  not  been  reached,  how- 
ever, and  this  should  stimulate  individual  research  and  study.  There 
are  rewards  yet  to  be  gained. 

If  this  book  proves  to  be  a  help  to  any,  and  stimulates  new  thoughts 
and  ideas,  it  will  not  have  failed  in  its  mission.  That  it  may  be  of  value 
is  the  sincere  wish  of  The  Author. 

New  York,  June  1st,   1903. 


;b^'' 


ERRATA. 

Pages  136,  137  and  138,  where  term  "compound  astigmatism"  is  used,  read 
"mixed  astigmatism." 

By  a  printer's  error,  cut  No.  .44  has  been  inserted  reversed. 
On   page  32   the   fourteenth   line   should   read:   "bent   from  the   perpendic- 
ular,"  etc. 

On  page  86  the  fourth  example  of  method  for  decentration  should  read: 
Prism.  Dioptres.  Millimetres. 

3"  6D.  ioX3=30H-6=S. 


CONTENTS 

Page. 
Introduction.  I 

CH.\PTER    I. 

Light.  5 

Energy  and  Radiant  Energy,  5.  Light.  7.  Wave  Theory  of  Light,  7.  Direction 
of  Light,  8.  Ray  and  Beam  of  Light,  9.  Pencil  of  Light,  10.  Luminous 
and  Ilkiminated  Bodies,  10.  Radiation  of  Lig;ht,  11.  Intensity  of  Light,  11. 
Absorption  of  Light,  12.  Transmission  of  Light,  12.  Reflection  of  Light, 
13.  Plane  Mirror.  14.  Inversion  by  Reflection.  15.  Multiple  Reflection, 
16.  Concave  Mirror:  Its  Centre  of  Curvature,  Vertex,  Aperture,  Principal 
Axis,  Principal  Focus,  17,  18.  Reflection  by  Concave  Mirror,  IQ.  Reflec- 
tion by  Convex  Mirror.  20.  Optical  Images  Described,  20.  Formation  of 
Image  by  an  Aperture,  21.  Formation  of  Image  by  a  Plane  Mirror,  22. 
Formation  of  Image  1)y  a  Concave  Mirror,  2^.  25.  Formation  of  Image 
by  a  Convex  Mirror,  25.  Diffusion  of  Light.  26.  Refraction  of  Light.  27. 
How  Refraction  Occurs.  29.  Refraction  by  Plane  Glass.  30.  Direction  of 
Refracted  Ray.  32.     Index  of  Refraction,  34.     Total  Reflection,  35. 

CHAPTER   II. 

Lenses.  36 

Optical  Prisms,  37.  Optical  Eflects  of  Prisms,  37.  Definitions  of  a  Lens,  39,  40. 
Convex  Spherical  Lens :  Its  Principal  Axis,  Secondary  Axis,  Optical 
Centre.  Principal  Focus,  39.  Conjugate  Foci.  41.  Formation  of  a  Real 
Image  by  a  Convex  Spherical  Lens,  41.  Position  and  Size  of  Image 
Created  by  a  Convex  Spherical  Lens,  42.  Formation  of  Virtual  Image 
by  a  Convex  Spherical  Lens,  42.  Magnification,  43.  Spherical  Aberration, 
44.  Types  of  Convex  Spherical  Lenses,  45.  Locating  the  Optical  Centre 
of  Spherical  Lenses,  46.  Characteristics  of  Convex  Spherical  Lenses, 
47,  49.  Decentration,  50.  Concave  Spherical  Lenses,  51.  Virtual  Focus,  51. 
Recognition  of  Convex  and  Concave  Spherical  Lenses.  53.  Dispersion  of 
Light.  53.  Refrangibility  of  Light,  53.  Chromatic  Aberration.  53.  The 
Spectrum.  53.  Inch  System  of  Measuring  Lenses.  54.  Dioptric  System,  56. 
Dioptric  and  Inch  Systems  Compared.  57.  Cylinder  Lenses,  60.  Definition 
of  Cylinder  Lenses.  62.  Maddox  Rod.  64.  Stenopaic  Disk,  65.  Pinhole 
Disk,  65.  Astigmatism.  66.  Combining  Cylinder  Lenses,  67.  Generic  and 
Contra-generic  Compounds,  68.  Recording  the  Axis  of  a  Cylinder  Lens, 
68.     Combining  Spherical  and  Cylinder  Lenses.  69.     Transposition,  Defini- 


tion  of,  71.  Theorems  to  Explain  Transposition,  71,  72.  Objective  De- 
monstration of  Transposition,  y^,  75.  Rules  for  Transposing,  76,  79.  Opti- 
cal Efifects  of  Cylindrical  Lenses.  80.  38.  Combining  Prisms  with  Spheri- 
cal, Cylindrical  or  Sphero-Cylinder  Lenses.  84,  85.  Systematic  Decentra- 
tion  for  Prism  Effect,  86.  87.     Neutralizing  Lenses.  87.  90. 

CHAPTER     in. 

Physical   Optus.  91 

Formation  of  Real  Optical  Images,  92.  Refracting  Systems,  92.  Achromatic 
Lenses,  92.  E.xperiments  in  Formation  of  Images  with  Convex  Spherical 
Lenses,  93,  96.  Experiments  with  Astigmatic  Refracting  Systems,  96,  98. 
Astigmatism  by  Incidence,  98.  The  Photographic  Camera,  98.  Stereoscopic 
Pictures,  99. 

CHAPTER    IV. 

Physiology   and   Anatomy'. 
General  Description  of  the  Eye  and  Its  Appendages. 

CHAPTER    V. 

Physiological    Optics.  106 

Comparison  of  the  Eye  with  a  Camera,  107.  The  Normal  Eye.  107.  109.  Ac- 
commodation, 109.  Range  of  Accommodation,  iii.  Amplitude  of  Ac- 
commodation, III.  Theories  of  Accommodation,  114,  115.  Line  of  Vision, 
n6.  Fixation,  116.  Field  of  Vision,  116.  Binocular  Vision,  117.  Ortho- 
phoria, 117.  Heterophoria,  117.  Convergence.  117.  Visual  Acuity,  118,  119. 
Measuring  and  Recording  Visual  Acuity.  120.  122  Emmetropia,  122. 
Errors  of  Refraction,  122.  Ametropia,  u;,  I  lyiH-imctropia,  128.  Cor- 
rection of  Hypermetropia,  130.  The  acti'Mi  ..i  ilu  \i  rotnmodation  in  Hy- 
permetropia,  131.  Convergent  Stabismu;-.  liJ  M>Mi,ia,  130.  Correction 
of  Myopia,  133.  The  Full  Correction  in  .Myopia.  135.  -Astigmatism  and 
Its  Corrections,  T35,  139.  Astigmatism  With  and  A.gainst  the  Rule.  130. 
Symmetrical  and  Assynietrical  Axes,  139.  Presbyopia,  139.  Donder's 
Definition  of  Presbyopia  and  Rule  for  Its  Correction,  140.  141.  .Anisome- 
tropia. 141.     The  "Dominant  Eye."  141.     Asthenopia,  142. 

CHAPTER    VI. 

Retinoscopy.  145 

Systems  of  Eye  Testing  and  Eye  Examination.  14s.  Subjective  and  Objective 
Methods,  146,  148.  Retinoscopy,  148.  The  Retinoscope,  150.  The  Light 
Source,  151.  The  Emergent  Rays,  151,  157.  Conjugate  Foci  of  the  Eye, 
158,  159.  Positive  Conjugate  Foci.  159.  Virtual  Conjugate  Foci,  159. 
Myopic    Far-Point,    159.     Working    Distance    in    Retinoscopy,    159.     Self- 


Luminous  Retinoscope,  i6i.  Working  Conditions  in  Retinoscopy  Ex- 
plained by  Diagrams,  161,162,  163.  Theory  of  the  Working  Distance  Ex- 
plained by  Analogy,  163.  Actual  Practice  Demonstrations,  164.  The 
Model  Eye  for  Practice  of  Retinoscopy,  165.  Positions  of  Patient  and 
Operator  Described,  166.  Cycloplegic  Not  Necessary,  166.  Light  Condi- 
tions of  the  Refracting  Room,  168.  Method  of  Control  of  the  Retinoscope, 
168.  The  Light  Area  on  the  Face,  171.  Transit  of  the  Pupil,  171.  The 
Luminous  Pupil  and  Retinal  Reflex,  172,  175.  The  Shadow :  Its  Variety  of 
Fiirm.  172.  The  Astigmatic  Liglit  Band,  173.  Directions  for  Actual 
Practice,  174.  175.  Movement  of  Light  Area  on  the  Face  and  That  of  the 
Reflex  in  the  Pupil,  176,  Choked  Appearance  of  the  Reflex,  176.  Reflex 
Movement  Indicative  of  Refraction,  177.  Character  of  Image  Observed  With 
the  Retinoscope,  179.  Rate  of  Movement  Dependent  Upon  Degree  of  Error, 
180.  Illustrative  Cases,  180,  181,  182,  1S3.  Determination  of  Myopic  Far-point 
Without  a  Lens,  183.  Procedure  in  Ca^c^  nf  A^ti,L;matism,  183.  Location  of 
the  Two  Principal  Meridians  in  .\>ti'-;iiiati-m,  1S4.  The  Value  of  the  Cor- 
recting Cylinder  Not  Altered  by  Allowance  for  \\(,rking  Distance,  186.  Illus- 
trative Cases  of  Astigmatism,  186,  187,  Procedure  in  Mixed  Astigmatism,  188. 
Explanation  of  "Scissors  Motion"  Observable  With  the  Retinoscope,  189. 
Irregular  Astigmatism,  189. 

CHAPTER    VII. 

Practical  Hints  fqr  the  Practice  of  Retinoscopy. 

Working  Out  Correction  of  Both  Eyes  Simultaneously,  190.  To  Avoid  Annoyance 
of  the  Patient  With  the  Light  Beam  F'rom  the  Retinoscope,  190.  Advisability 
of  Conducting  Retinoscopic  Examination  as  Speedily  as  Possible,  190.  The 
After  Effects  of  the  Light  From  the  Retinoscope  Upon  the  Eye  of  the  Patient, 
191.  Selection  of  Retinoscope,  191.  Spherical  Aberration  of  the  Eye,  How 
It  Affects  the  Retinoscopic  Estimate  of  Refraction,  191.  Irregular  Refraction 
of  the  Eye,  How  It  Affects  the  Retinoscopic  Estimate  of  Error,  191.  The 
Value  of  the  Retinoscopic  Estimate,  as  Aft'ected  by  Large  Pupils,  191.  The 
Value  of  the  Luminous  Retinoscope  Compared  to  the  Older  Forms,  192. 
Subjective  Work  With  the  Test  Case,   192. 


INTRODUCTION. 

TT  seems  hardly  possible  that  in  this  period  of  advanced  thought  and 
-■-  research,  when  almost  every  branch  of  human  industry  is  con- 
ducted along  scientific  lines;  that  so  important  a  profession,  as 
that  whose  followers  practice  the  adapting  of  lenses  to  correct  de- 
fects of  vision,  has  up  to  within  a  few  years  been  guess  work. 

Is  the  term  not  advisedly  used  when  an  operator  orders  glasses 
for  a  person,  taking  as  a  basis  for  his  calculations,  the  unverified 
statements  of  the  person  as  to  what  he  c£»n  see  with  this  or  that  lens, 
or  combination  of  lenses  ?  A  person  may  be  conscientious  in  his 
replies,  but  may  not  have  understood  the  query;  again,  in  complicated 
cases,  where  various  combinations  of  lenses  have  been  tried,  the 
ability  to  differentiate  becomes  fogged.  The  replies  of  illiterates, 
children  and  foreigners  are  not  to  be  depended  upon.  What 
basis  of  certainty  then  do  such  methods  afford;  what  assurance  has 
the  operator  that  his  formula  is  even  approximately  correct  ? 

A  science  is  founded,  not  upon  uncertainties,  but  upon  facts; 
therefore,  subjective  examination  of  the  eye  is  not  scientific,  though 
we  grant  that  it  has  its  place  and  should  be  used.  It  is  only  within 
the  past  few  years,  that  the  diagnosis  of  errors  of  refraction  and  their 
correction  by  the  use  of  glasses  has  been  scientific.  Examination 
being  conducted  objectively,  the  refractive  condition  of  the  eye  is 
ascertained  by  comparison  of  actual  conditions  with  a  known  standard. 
This  work  is  a  departure  from  the  usual  style  of  optical  text  books 
and  is  based  upon  methods  employed  by  the  author  in  successful  daily 
practice.  The  subject  of  lenses  and  their  properties  is  dealt  with  as 
fully  as  possible,  as  it  is  necessary  in  order  to  understand  ocular 
refraction,  to  be  familiar  with  this  subject.  The  refractive  media  of 
the  eye  is  eqviivalent  to  a  lens. 

It  may  be  said  at  first  glance  that  too  much  time  is  devoted  to 
subjects  that  have  little  relation  to  optics,  that  the  optical  student 
need  not  bother  with  such  topics.  The  answer  is,  that  time  spent  in 
the  study  of  any  subject  that  is  in  any  way  related  to  optics,  is  time 
well  spent.  The  optician  must  not  fear  to  know  too  much  but  too 
little. 

The  famous  address  delivered  by  Helmholtz  in  1871,  at  Heidel- 
berg, shows  upon  what  a  broad    basis   of  knowledge  his  intellectual 


2  OCULAR         K  E   I-    K  A  C  T  I  O  N. 

power  was  founded.  A  portion  of  it  is  quoted ;  the  whole  of  it  is  well 
worth  reading,  it  should  stimulate  the  optical  student  to  higher  aims. 

'•The  Mystery  of  Creation." — "All  life  and  all  motion  on  our  earth, 
is,  with  few  exceptions,  kept  up  by  a  single  force,  that  of  the  sun's 
rays,  which  bring  us  light  and  heat.  They  warm  the  air  of  the  hot 
zones;  this  becomes  lighter  and  ascends,  while  the  colder  air  flows 
toward  the  poles.  Thus  is  formed  the  great  circulation  of  the  passage- 
winds.  Local  differences  of  temperature  over  land  aud  sea,  plains 
and  mountains,  disturb  the  uniformity  of  this  great  motion,  and  pro- 
duce for  us  the  capricious  change  of  winds.  \Varm  aqueous  vapors 
ascend  with  the  warm  air,  become  condensed  into  clouds,  and  fall  in 
the  cooler  zones,  and  upon  the  snowy  tops  of  the  mountains,  as  rain 
and  as  snow.  The  water  collects  in  brooks  and  rivers,  moistens  ihe 
plains  and  makes  life  possible;  crumbles  the  stones,  carries  their 
fragments  along,  and  thus  works  at  the  geological  transformation  of 
the  earth's  surface.  It  is  only  under  the  influence  of  the  sun's  rays 
that  the  variegated  covering  of  plants  of  the  earth  grows;  and  while 
they  grow,  they  accumulate  in  their  structure  organic  matter,  which 
partly  serves  the  whole  animal  kingdom  as  food,  and  serves  man 
more  particularly  as  fuel.  Coals  and  lignites,  the  sources  of  power 
of  our  steam  engines,  are  remains  of  primitive  plants,  the  ancient 
production  of  the  sun's  rays. 

"Need  we  wonder  if  to  our  forefathers  of  the  Aryan  race,in  India 
and  in  Persia,  the  sun  appeared  as  the  fittest  symbol  of  the  Diety  ? 
They  were  right  in  regarding  it  as  the  giver  of  all  life — as  the  ultimate 
source  of  almost  all  that  has  happened  on  earth. 

"But  whence  does  the  sun  acquire  this  force?  It  radiates  forth  a 
more  intense  light  than  can  be  attained  with  any  terrestial  means. 
It  yields  as  much  heat  as  if  fifteen  hundred  pounds  of  coal  were 
burned  every  hour  upon  each  square  foot  of  its  surface.  Of  the  heat 
which  thus  issues  from  it,  the  small  fraction  which  enters  our  atmos- 
phere furnishes  a  great  mechanical  force.  Every  steam  engine  teaches 
us  that  heat  can  produce  such  force.  The  sun,  in  fact,  drives  oh  earth 
a  kind  of  steam  engine  whose  performances  are  far  greater  than  those 
of  artificially  constructed  machines.  The  circulation  of  water  in  the 
atmosphere  raises,  as  has  been  said,  the  water  evaporated  from  the 
warm  tropical  seas,  to  the  mountain  heights;  it  is,  as  it  were,  a  water 
raising  engine  of  the  most  magnificent  kind,  with  whose  power  no 
artificial  machine  can  be  even  distantly  compared.  I  have  previously 
explained  the  mechanical  equivalent  of  heat.  Calculated  by  that 
statrlard,  the  work  which  the  sun  produces  by  its  radiation  is  equal  to 


INTRODUCTION".  3 

the  constant  exertion  of  seven  thousand  horse  power  for  each  square 
foot  of  the  sun's  surface. 

"  For  a  lon.sftime  experience  had  impressed  on  our  mechanicians 
that  a  working  force  cannot  be  produced  from  nothing-;  that  it  can  only 
be  taken  from  the  stores  which  nature  possesses,  which  aie  strictly 
limited,  and  which  cannot  be  increased  at  pleasure — whether  it  be 
taken  from  the  rushing  water  or  from  the  wind;  whether  from  the 
layers  of  coal,  or  from  men  and  from  animals,  which  cannot  work 
without  the  consumption  of  food.  Modern  physics  has  attempted  to 
prove  the  universality  of  this  experience,  to  show  that  it  applies  to 
the  great  whole  of  all  natural  processes,  and  is  independent  of  the 
special  interests  of  man.  These  have  been  generalized  and  compre- 
hended in  the  all  ruling  natural  law  of  the  conservation  of  force. 
No  natural  process,  and  no  series  of  natural  processes,  can  be  found, 
however  manifold  may  be  the  changes,  which  take  place  among  them, 
by  which  a  motive  force  can  be  continuously  produced,  without  a  cor- 
responding consumption.  Just  as  the  human  race  finds  on  earth  but 
a  limited  supply  of  motive  forces,  capable  of  producing  work,  which 
it  2an  utilize  but  not  increase,  so  also  must  this  be  the  case  in  the 
great  whole  of  nature.  The  universe  has  its  definite  store  of  force, 
which  works  in  it  under  ever- varying  forms ;  is  indestructable,  not  to 
be  increased,  everlasting  and  unchangeable  like  nature  itself." 

It  is  the  author's  conviction,  that  the  greatest  success  at  present 
is  being  made,  and  in  the  future  will  be  attained,  by  that  class  of 
operators,  oculists  and  opticians,  who  make  retinoscopy  the  corner- 
stone of  the  adapting  of  lenses  to  the  correction  of  refractive  errors. 
The  aim  of  the  work  will,  therefore,  be  to  teach  the  fundamental 
principles  of  retinoscopy,  to  fit  the  student  to  intelligently  use  the 
retinoscope  in  diagnosmg  errors  of  refraction.  The  great  difficulty 
with  operators  of  the  instrument  is,  that  while  they  know  that  certain 
phenomena  occur,  they  do  not  understand  the  cause  of  such,  hence 
their  indifferent  success  in  its  use. 

The  method  of  teaching  is  as  far  as  possible  objective ;  a  law  is 
given  in  as  simple  yet  comprehensive  form  as  possible,  followed  by 
experiments  or  demonstrations  to  prove  it;  the  student  should  make 
these  for  himself. 

A  well  known  educator  once  said: — "It  is  a  cardinal  principle  in 
modern  pedagogy  that  the  mind  gains  a  real  and  adequate  knowledge 
of  things  only  in  the  presence  of  things  themselves.  Hence  the  first 
step  in  all  good  teaching  is  an  appeal  to  the  observing  powers.  The 
subject  studied  and  the   studying   mind  are  placed  in  the  most  direct 


4  OCULAR         REFRACTION. 

relations  with  one  another  that  circumstances  admit.  Words  and 
other  symbols  are  not  allowed  to  intervene,  tempting  the  learner  to 
satisfy  his  mind  with  ideas  obtained  at  second-hand." 

The  use  of  analogy  is  resorted  to  at  times  that  students  may  find  it 
easier  to  comprehend  and  memorize  facts.  The  field  of  optical  inves- 
tigation is  large,  and  each  should  feel  that  he  has  just  as  good  an  op- 
portunity as  another  to  make  some  valuable  discovery;  certainly  his 
investigadons  will  yield  him  personally  good  returns. 

The  author  acknowledges  assistance  received  from  the  writings 
of  Francis  Valk,  M.D.,  of  New  York,  Alfred  P.  Gage,  A.M.,  of  Bos- 
ton, Prof.  Ira  Remsen,  of  Johns  Hopkins  University,  Baltimore,  and 
others. 

That  the  work  is  complete  and  without  fault  is  not  claimed,  but 
that  it  may  be  of  some  service  in  advancing  the  science  of  ocular 
refraction  is  the  wish  of  the  author. 

March  8,  1902. 


CHAPTER    I. 


LIGHT. 


Cnergy  ts  that  ivJiich  creates,  destroys,  or  changes  viotioji;  it  is  power 
■^—^      in  action. 

It  is  conclusively  proved  that  the  store  of  energy  in  the  universe 
is  constant,  none  can  be  created,  none  is  destroyed ;  it  is  merely  trans- 
formed from  one  form  into  another,  each  bearing  a  definite  relation  to 
the  other;  this  is  termed  the  correlation  of  forces  and  the  conservation 
of  energy.  We  are  accustomed  to  think  of  energy  as  power  to  do 
work;  it  assumes  various  forms,  mechanical,  chemical,  electrical 
energy,  etc.  While  there  is  no  loss  of  actual  energy  in  transforma- 
tion, there  is  a  loss  of  available  energy,  a  portion  taking  the  form  of 
heat  expended.  The  steam  engine  transforms  chemical  energy  stored 
in  coal  into  mechanical  energy;  the  turbine  transforms  energy  stored 
in  water,  due  to  its  position,  into  mechanical  energy;  the  dynamo 
transforms  mechanical  into  electric  energy,  which  is  transformable 
into  light,  heat  and  motion. 

A  good  example  of  the  transformability  of  energy,  is  furnished 
by  the  electric  cars  on  our  streets;  they  are  propelled,  lighted  and 
heated  from  the  same  source. 

The  principal  sources  of  energy  stored  upon  the  earth  and  avail- 
able to  the  use  of  man,  are  the  processes  of  combustion,  coal,  wood, 
oil,  etc. ;  water  in  motion,  and  at  an  elevation,  thus  available  through 
gravitation;  air  in  motion  The  source  of  all  energy  on  the  earth  is, 
with  few  exceptions,  the  rays  of  the  sun. 

That  form  which  is  manifested  as  heat  and  is  termed  radiant 
energy,  is  that  which  makes  possible  the  science  of  optics. 

Every  body  gives  off  radiant  energy  regardless  of  its  tempera- 
ture. It  is  manifested  by  the  propagation  in  the  ether  of  waves  that 
transmit  tr.e  radiant  energy  to  other  bodies,  these  may  in  turn  send  it 


6  OCULAR         R  E  F  R  A   C  T  I  0  N. 

to  Still  Other  bodies.  These  waves  are  of  different  length,  those  sent 
out  by  a  cold  body  being  longer  than  those  of  a  hot.  In  the  lower 
temperatures  the  waves  are  of  such  length  that  they  make  no  impres- 
sion upon  the  eye,  and  we  recognize  them  merely  as  heat.  At  about 
1080°  Fahrenheit  a  body  radiates  energy  that  causes  it  to  emit  a  red 
glow,  and  is  said  to  be  luminous,  radiating  rays  of  red  light.  As  the 
temperature  becomes  higher,  the  waves  are  shorter  and  shorter,  and 
the  various  colors  of  the  spectrum  in  regular  order  are  radiated,  until 


at  about  2700°  Fahrenheit,  all  the  colors  of  the  spectrum  are  radiated 
and  the  body  is  said  to  be  white  hot.  When  in  this  conditio!,  the 
radiant  energy  given  off  by  a  body  is  called  light. 

The  eye  is  adapted  to  perception  of  waves  of  certain  lengths,  they 
are  those  that  produce  the  colors  of  the  spectrum;  red,  orange,  yellow, 
green,  blue  and  violet;  those  having  greater  and  less  length  than 
these,  do  not  affect  the  eye,  therefore,  in  the  study  of  ocular  refraction 
we  need  not  consider  them.  The  effect  these  waves  produce  upon  the 
eye  is  called  sight.     The  velocity  of  light  is  about    is6,ooo  miles  in  a 


second;  thus  it  is  easy  to  understand  how  we  can  so  quickly  see  any 
object,  no  matter  what  its  distance,  as  soon  as  we  direct  our  eyes 
toward  it;  the  light  it  sends  to  the  eyes  traverses  the  intervening- 
space  in  an  inconceivably  small  fraction  of  time.  An  illustration  of 
the  rapidity  with  which  light  travels,  as  compared  to  that  of  sound, 
is  seen  by  the  puff  of  steam  from  the  whistle  of  a  distant  locomotive, 
followed  by  the  sound  some  time  later;  and  the  flash  of  a  gun  and  its 
report.  Sound  waves  traverse  the  air  at  the  rate  of  but  i,ioo  feet  in 
a  second. 

Light  is  that  part  of  radiant  energy,  by  means  of  which,  through  its 
action  upon  the  eye,  we  are  enabled  to  see  the  object  from  zvhich  it  proceeds. 
That  light  is  a  form  of  energy,  and  as  such  can  produce  motion,  is 
illustrated  by  an  instrument  called  the  radiometer;  (Fig.  i.)  It  con- 
sists of  two  crossed  arms  in  the  shape  of  a  vane,  at  the  extremity  of 
each  of  the  arms  is  a  small  disk  of  aluminum,  blackened  on  one  side, 
white  on  the  reverse.  This  vane  is  delicately  poised  and  is  rotatable 
on  a  pivot,  is  inclosed  in  a  glass  bulb  from  which  the  air  has  been  ex- 
hausted. Exposed  to  the  light,  the  vane  revolves,  the  white  faces  of 
the  disks  in  advance;  the  stronger  the  light  the  more  rapid  the  motion 
of  the  vane.  Motion  is  created  where  energy  is  applied,  therefore, 
energy  must  be  exerted  upon  the  vane  in  a  certain  way.  Now,  as 
energy  must  have  some  medium  through  which  to  act,  something 
must  remain  inside  the  bulb  after  the  air  is  exhausted. 

It  is  now  generally  accepted  as  a  fact  that  there  exists  in  all 
space  a  certain  medium,  to  which  has  been  given  the  name  Ether;  that 
it  penetrates  everywhere,  that  radiant  energy  causes  it  to  vibrate  and 
imparts  to  it  a  wave-like  motion,  that  to  certain  of  these  waves,  the 
eye  is  sensitive.      This  is  the  wave  or  undulation  theory  of  light. 

It  is  only  by  assuming  the  existence  of  some  medium  capable  of 
transmitting  light  between  objects,  much  in  the  same  way  that  air 
transmits  sound,  that  we  can  account  for  the  actions  of  light.  Some 
thing  cannot  be  evolved  from  nothing,  neither  can  space  that  contains 
nothing  communicate  sound  or  light  between  distant  points.  This 
ether  is,  therefore,  assumed  to  fill  all  space,  penetrating  all  liquids 
and  solids,  and  surrounding  every  molecule  of  matter  in  the  universe, 
just  as  the  air  envelops  the  earth.  The  air  surrounding  the  earth  is 
comparatively  a  thin  belt,  so  that  ether  fills  the  interplanetary  space. 
This  theory  of  the  existence  of  ether  links  light  and  sound  intimately, 
each  acting  through  a  medium  by  the  propagation  of  waves,  and  in 
the  study  of  light  the  student  will  find  it  helpful  to  an  understanding 
of  the  various  phenomena  if  he  has  some  knowledge  of  sound.     As  air 


OCULAR 


ACTION. 


and  sound  are  more  tangible  than  ether  and  light  he  may  use  the  an- 
alogy for  study  purposes. 

We  are  compelled  to  accept  certain  things  as  facts,  reasoning 
upon  a  basis  of  cause  and  effect,  thus:  We  do  not  know  that  a  dumb 
animal  can  see  and  hear,  but  we  accept  it  as  a  fact,  because  it  acts  as 
if  it  does,  for  upon  no  other  basis  can  we  explain  certain  of  its  actions. 
Following  this  line  of  reasoning  we  can  safely  accept  the  theory  of 
the  existence  of  ether  until  it  is  disproved. 

Light  itself  is  invisible,  but  objects  within  its  path  are  rendered  vis- 
ible by  the  light  they  reflect. 

Darken  a  room  and  admit  the  sunlight  through  a  small  round 
hole,  the  light  is  not  visible,  but  its  path  is  easily  traced  by  the  dust 
particles  floating  in  the  air  and  crossing  its  path  are  illuminated. 
Where  the  light  strikes  the  floor  or  wall  a  small  round  spot  will  be 
seen,  due  to  its  illumination,  but  the  room  remains  dark.  If  there 
were  no  such  dust  particles  or  other  objects  in  the  room  to  obstruct 
its  path  it  could  not  be  traced,  but  only  the  point  where  it  strikes 
would  be  seen.  The  path  the  light  traverses  in  the  room  will  be 
found  to  be  straight. 

Light  always  travels  in  a  straight  line. 

Take  a  cigar  box,  and  having  removed  one  end,  replace  it  with 
ground  glass,  L  M  N  O  (Fig.  2),  make  a  small  round  hole  A  exactly  in 
the  centre  of    the  other  end.     On    the  bottom  glue  at  intervals  small 


Figure  2. 

Device  to  prove  that  the  path  of  light  is  straight. 

strips  of  wood  in  pairs,  spaced  close  enough  to  hold  a  card,  parallel 
to  the  ground  glass.  Cut  several  cards  to  just  fit  inside  the  box  in 
these  slots,  in  the  centre  exactly  of  each  make  a  hole  the  size  of  the 
one  in  the  box  at  A.  Place  three  or  more  of  these  cards  C  in  the  slots 
made  to  hold  them.  Darken  a  room  and  place  a  lighted  candle  in  the 
centre  of  it;  from  any  position  in  the  room,  by  directing  the  aperture 
in  the  box  toward  the  candle,  a  spot  of  light  will  appear  in  the  centre 


of    the  ground  glass.     As    the  holes  in  the  cards  and  the  front  of    the 

box  are  in  line,  the  path  of  the  light  through  the  box  must  be  straight. 

Substitute  for  one  of   the   cards  now  in  the  box  one  in  which  the 

hole   is   not   in  the  centre;  no  light  will  now  appear  upon  the  glass. 


Figure  3. 

the  propagation  of 


,■,  L  L  . 


Diagram  to  illu 

This  not  only  proves  that  light  travels  in  a  straight  line,  but  also  that 
it  cannot  deviate  from  it. 

A  ray  is  the  smallest  conceivable  amount  of  light;  it  is  propagated 
along  a  line  that  is  perpendicular  to  the  wave  front  at  the  point  of 
intersection. 


Formation  of  a  beam  of  light. 

Figure  3  represents  a  line  L  L'  perpendicular  to  the  wave  W  F; 
at  the  point  of  intersection  X,  it  indicates  the  path  of  a  light  ray  from 
L  toL'. 

A  beatn  is  a  collection  of  rays  whose  paths  are  parallel. 

Figure  4  represents  parallel  rays  intersecting  the  wave  W  F 
perpendicularly;  it  is  seen  that  this  can  occur  only  where  the  surface 
of  the  wave  is  a  plane  at  the  points  of  intersection. 


,o  O  C   U    L  A   K         K   K   F   R  A  C   T  I  O   N. 

A  pencil  is  a  collection  of  rays  whose  paths  meet  at  a  common  point. 

Figure  5  represents  rays  cutting  the  wave  W  F  perpendicularly 
at  the  points  of  intersection.  As  the  surface  of  the  wave  is  not  a 
plane  the  rays  cannot  be  parallel,  and  if  prolonged  must,  therefore, 
meet  at  some  point,  which  we  will  assume  to  be  at  P. 

Light  makes  objects  visible,  some  by  means  of  that  which  they 
create,    as   a   candle   flame,   electric  light,    the    sun,    etc.;   these    are 


Figure  5. 
Formation  of  a  pencil  of  light. 

termed  luminous  bodies.  Other  bodies  are  rendered  visible  when 
they  receive  light  from  luminous  bodies,  in  which  state  they  are  said 
to  be  illuminated,  as  trees,  houses,  etc. 

Luminous  bodies  emit  light  in  all  directions  equally  and  from  every 
point  of  their  surface. 

Take  a  tin  can  and  punch  holes  around  it  with  a  small  round 
wire  nail,  place  a  lighted  candle  inside  and  take  it  into  a  darkened 
room.  It  will  be  observed  that  light  is  emitted  from  all  the  holes 
alike.  By  looking  thiough  any  of  the  holes  various  points  of  the 
candle  flame  will  be  seen,  showing  that  every  point  is  an  independent 
source  of  light;  this  makes  possible  the  formation  of  images.  The 
experiment  illustrated  by  figure  2  also  demonstrates  this. 

Rays  of  light  given  off  by  luminous  and  illuminated  objects  are  divergent, 
never  convergent,  unless  rendered  so  by  some  applied  condition,  and  are  only  the- 
oretically parallel  when  they  come  from  a  distance  of  twenty  or  more  feet. 

Figure  6  represents  a  candle  L  and  rays  of  light  radiating  from  it 
in  all  directions  showing  their  divergency.  The  angle  N  L  O,  made 
by  the  rays  N  and  O,  is'less  than  the  angle  M  L  P,  made  by  the  rays 
M  and  P,  and  the  smaller  the  angle  formed  by  two  straight  lines  the 
nearer  they  approach  being  parallel ;  therefore,  the  rays  N  O  are 
nearer  parallel  than  M  P,  but  M  P  are  more  divergent  than  N  O,  and 
R  P  are  still  more  divergent  than  M  P.  This  diagram  illustrates  why 
no  two  rays   from   the    same  point  can  be  parallel.      Place  a  card  per- 


pendicular  to  the  base  line  upon  which  the  candle  is  fixed,  cutting  the 
rays  M  N  O.P  at  A  B  C  D.  Suppose  the  distance  from  B,  where  the 
ray  N  strikes  the  card,  to  C,  where  the  ray  O  strikes,  is  one  quarter  of 
an  inch,  and  a  hole  one  quarter  of  an  inch  in  diameter  be  made  in  the 
card,  all  the  rays  included  between  N  and  O  will  pass  through  the 
hole.     In  order   to  permit  the  rays  M  and  P  to  pass  through  the  same 


Figure  6. 
Radiation  of  light  in  all  directions  ;  divergency  of  the  rays. 

hole,  by  reason  of  their  greater  divergency,  it  would  be  necessary  to 
move  the  card  nearer  to  the  light,  to  say  D',  this  would  allow  rays  in- 
cluded between  M  and  P  to  pass  through.  This  experiment  demon- 
strates two  facts,  viz.:  that  rays  of  light  passing  through  a  given  aper- 
ture are  more  divergent  as  it  approaches  their  source,  that  the  num- 
ber of  rays  (or  the  amount  of  light)  passing  through  a  given  aperture 
decreases  as  it  is  removed  from  their  source. 


x-^ 


as: 


Figure  7. 

Variations  of  intensity  of  light  at  different  distances  from  its  source. 

The  intensity  of  light  decreases  as  the  square  of  the  distance  traversed 
increases,  •Caw'i/dit  twice  the  distance,  one-fourth  the  intensity ;  four 
times  the  distance,  one  sixteenth  its  intensity. 

Figure  7  represents  a  candle  L  placed  before  a  heavy  piece  of 
cardboard  C,  having  a  small  round  hole  at  A;  the  screen  of  white 
paper  S  held  back  of   C,  say  two  inches,  so  that  light  passing  through 


,2  OCULAR         R   E  F  K  A  C  T   I  O  N. 

A  will  fall  upon  S  and  make  a  round  spot  of  light  B.  Move  S  four 
inches  away  from  C  to  the  position  S'  and  note  the  size  of  the  spot  B' 
If  S  was  two  inches  from  C  and  the  diameter  of  B  was  three  inches, 
then  if  S'  be  placed  four  inches  from  C  the  diameter  of  B'  will  be 
six  inches,  just  twice  the  diameter  of  B.  Now,  as  the  areas 
of  any  two  circles  are  to  each  other  as  the  squares  of  their  diameters, 
the  area  of  B'  is  four  times  that  of  B,  and  as  each  receives  the  same 
amount  of  light,  for  the  positions  of  L  and  C  remain  the  same,  the 
intensity,  of  the  light  at  B'  is  only  one-fourth  that  at  B.  In  the  ex- 
periment made  with  the  apparatus  illustrated  by  figure  2  it  will  be 
found  that  the  nearer  the  light  is  approached,  the  brighter  the  light 
upon  the  ground  glass  will  appear,  the  further  it  is  removed  the 
fainter  the  spot  will  be. 

Light  exhibits  certain  phenomena;  it  is  absorbed,  transmitted, 
reflected,  diffused,  refracted,   etc. 

Tlie  effect  of  the  absorption  of  certain  light  rays  is  to  give  an  object 
color;  those  that  it  rejects  or  sends  to  the  eye  produce  the  effect  of  red, 
green,  blue,  etc.  Objects  that  absorb  none  of  the  light  rays,  but 
send  all  combined  to  the  eye  have  the  appearance  we  term  white; 
those  that  absorb  all  the  rays,  returning  none  to  the  eye,  appear  black, 
as  it  is  called.  The  term  blackness  or  darkness  means  an  absence  of 
light,  and  all  objects  are  black  in  the  dark.  An  object  to  appear  of  a 
certain  color  must  receive  light  of  that  color,  if  it  does  not  receive 
such  its  color  is  changed;  if  the  proper  color  of  light  combined  with 
other  light  colors  are  received,  those  for  which  it  is  not  adapted  are 
absorbed.  The  absorption  of  rays  of  light  warms  an  object,  as  it  con- 
verts them  into  heat,  thus:  Of  two  objects  receiving  the  same  light 
that  which  absorbs  the  most  light  rays  will  be  the  warmer,  while  that 
absorbing  the  lesser  number  of  rays  will  be  the  cooler.  This  explains 
why  people  living  in  tropical  countries  adopt  white  for  clothing;  it  is 
cooler  because  it  absorbs  little  light  energy. 

Rays  of  light  striking  the  surface  of  a  medium,  some  of  them  pass 
through  it  or  are  transmitted.  Different  bodies  offer  more  or  less  ob- 
struction to  the  passage  of  light  rays;  those  that  offer  little,  such  as 
air,  glass,  water,  crystal,  etc.,  are  termed  transparent;  those  that  per- 
mit but  a  portion  of  the  light  rays  to  pass  through,  such  asthin  paper, 
ground  glass,  etc,  are  termed  translucent;  those  that  do  not  permit 
the  passage  of  any  of  the  light  rays,  such  as  heavy  paper,  sheet  tin, 
etc.,  are  termed  opaque.  The  terms  transparent  and  opaque  are  not 
absolute,  for  all  substances  offer  some  obstruction  to  the  passage  of 
light,  while  none  completely  obstruct  it.     Even  air  does  not  transmit 


all  rays   of  light    from    a   given    source,  and    iron  rolled  thin  enough 
transmits  an  appreciable  amount  of  light. 

The  rays  of  light  that  are  not  transmitted  on  striking  the  surface 
of  a  medium  are  bent  back  into  the  medium  through  which  they 
came,  they  are  said  to  be  reflected.  The  rays  approaching  and  strik 
ing  the  surface  of  a  medium  are  called  the  ?■«<:/(/«//' r^'ji'.s-;  those  that 
are  bent  back  into  the  medium  whence  they  came  are  called  the 
reflected  rays. 


Perpendicular  refls 


Figure  8. 

clion  of  light  ;   I  C,  incident 


»y:  C 


^fleeted  ray. 


Light  rays  striking  the  surface  of  a  medium  perpendicularly  and 
reflected,  traverse  the  same  path  by  which  they  approached;  they.are, 
therefore,  reflected  to  their  source. 

Figure  8  represents  a  medium  M,  the  incident  ray  I  strikes  the 
surface  A  B  at  C;  I  C  is  perpendicular  to  A  B,  and  the  path  of  the 
incident  ray  is  from  I  to  C  in  a  straight  line,  that  of  the  reflected  ray 
is  also  in  a  straight  line  from  C  to  I,  or  back  to  its  source. 


Light  rays  striking  the  surface  of  a  medium  in  any  direction  other 
than  perpendicular  to  its  surface  at  the  point  of  incidence  and  reflected, 
the  incident  rays  form  an  angle  with  the  perpendicular  which  is  called 
the  angle  of  incidence.     The  reflected  rays  form   an  angle  also  with 


14  O  C   U   L  A  K         1<   E   V    R   A  C   T   1   O  N. 

the  perpendicular  called  the  angle  of  reflection.  T/w  angle  of  incid- 
ence and  the  angle  of  reflection  are  ahvays  equal. 

In  figure  9,  I  is  the  incident  ray  striking  the  surface  C  D  at  B  and 
reflected  to  R;  A  B  is  the  perpendicular  to  C  D  at  B.  The  angle  of 
incidence  1  B  A  is  equal  to  the  angle  of  reflection  R  B  A.  To  find 
the  direction  that  a  reflected  ray  will  take  it  is  only  necessary  to  erect 
at  the  point  of  incidence  a  perpendicular,  ascertain  the  angle  of  in- 
cidence and  construct  the  angle  of  reflection  equal  to  it. 

Into  a  darkened  room  admit  a  pencil  of  light  through  a  small  hole, 
place  a  mirror  so  as  to  receive  it  obliquely  upon  its  surface.  The  light 
is  reflected,  according  to  the  law  of  reflection,  in  a  given  direction,  and 
by  placing  the  eye  in  the  path  of  the  reflected  pencil  an  image  of  the 
source  of  the  light  is  seen  upon  the  mirror,  and  not  the  mirror.  If  the 
mirror  be  covered  with  a  piece  of  white  cardboard,  the  source  of  the 
light  cannot  be  seen;  though  the  incident  pencil  follows  the  same  cer- 
tain direction  as  before,  some  change  takes  place  at  the  point  of  in- 
cidence, the  reflected  pencil  does  not  follow  any  definite  direction,  it 
is  broken  up,  and  the  various  rays  are  reflected  in  all  directions.     This 


Kelleclion  by : 

renders  the  cardboard  visible  from  any  position  in  the  room.  The 
phenomon  is  due  to  the  difference  in  the  reflecting  surfaces.  A 
smooth  surface  reflects  light  in  a  definite  direction,  creates  an  image 
of  the  object  from  which  the  rays  proceed,  and  is  called  a  mirror.  A 
rough  surface  scatters  the  light,  illuminates  adjacent  objects,  and  does 
not  create  an  image.  The  best  mirrors  are  polished  metal  surfaces  and 
smooth  gla.=s  backed  with  an  opaque  substance. 

The  pencil  of  light  composed  of  the  rays  R,  figure  10,  strikes  the 
surface  of  the  mirror  A  B,  and  is  reflected  in  a  definite  direction  R'. 
This  is  due  to  the  fact  that  all  points  in  the  surface  A  B  lie  in  the 
same  plane.     An  image  is  created  by  the  surface  A  B. 


I.    I   G   li   T.  15 

The  amount  of  light  that  a  smooth  surface  reflects  increases  with 
the  angle  of  incidence. 

A  B,  figure  11,  represents  a  plane  mirror  in  a  horizontal  position, 
above  it  is  placed  the  goblet  L.  Looking  from  the  position  E  at  the 
goblet  reflected  in  the  mirror,  it  appears  to  be  inverted  and  situated  at 
L'.  Every  point  upon  the  goblet  sends  out  light  which  is  reflected  to 
the  eye.  Let  C  F  and  D  G  represent  divergent  rays  of  light  from  the 
points  C  and  D;  erect  perpendiculars  P  P  to  the  surface  A  B  at  the 
points  of  incidence  F  and  G.     By  constructing  the  angles  of  incidence 


A 


Figure  II. 

Inversion  ot  the  image  by  reHection  of  a  horizontal  plane  mirror. 

and  reflection,  the  paths  of  F  E  and  G  E  are  found.  By  this  it  is 
shown  that  divergent  rays  reflected  by  a  plane  mirror  continue  diver- 
gent after  reflection;  in  the  same  manner  it  can  be  demonstrated  that 
parallel  and  convergent  rays  reflected  by  a  plane  mirror  continue  par- 
allel or  convergent  after  reflection.  Figure  10  shows  that  parallel  rays 
reflected  by  a  plane  mirror  are  parallel  after  reflection.  To  the  eye  the 
position  of  an  object  appears  to  be  in  the  direction  from  which  the  rays 
of  light  enter  the  eye.  By  prolonging  the  lines  E  F  and  E  G  they  will 
meet  at  the  points  C'  and  D',  showing  why  L  appears  to  be  placed  at 
L'  and  why  inverted.  This  is  called  a  virtual  image  of  an  object  be- 
cause it  is  not  a  real  image.  A  virtual  image  formed  by  a  plane  mirror 
is  a  reproduction  in  size  and  shape  of  the  object  reflected,  and  is  the 
same  distance  behind  the  mirror  as  the  object  is  in  front  of  it.  This 
fact  is  frequently  utilized  to  reflect  a  test  chart  placed  at  the  back  of  a 
person  in  the  operating  room.     The  chart   must  be  printed  in  reverse. 


i6 


o  c  u 


A   R 


REFRACTION. 


The  mirror  doubles  its  distance,  as  the  eye,  instead  of  receiving  incident 
rays  from  the  chart,  receives  reflected  rays ;  the  light  traversing  the 
space  lietween  the  chart  and  the  mirror  and  back  again  to  the  eye  of 
the  patient. 

Objects  reflected  by  a  horizontal  plane  mirror  are  inverted,  thus: 
Trees  on  the  banks  of  a  stream  or  lake  reflected  by  the  surface  of  the 
water  appear  to  be  growing  downward  into  the  water.  Objects  re- 
flected by  a  vertical  plane  mirror  are  reversed,  thus:  In  looking  into 
.such  a  mirror  one's  right  hand  appears  to  be  the  left.  When  a  plane 
mirror  is  tipped  away  from  a  vertical  or  horizontal  plane,  objects  re- 
flected by  it  form  an  angle  with  the  horizon  that  is  dependent  upon 
the  angle  of  the  mirror. 

Let  A  B,  figure  12,  represent  a  piece  of  thick  plate  glass  mirror; 
L,  a  pencil  of  light  striking  the  surface  obliquely  at  C,  is  reflected  to 
D;  all  the  light,  however,  is  not  reflected  at  C,  a  portion  of  it  is  trans- 
mitted   by  the    glass  to    K,  from    K  it  is  reflected  to  E,  and  a  portion 


Figure  12. 

Principle  of  multiple  refle 


continues  to  F;  that  which  does  not  pass  from  the  glass  at  E  is  reflect- 
ed to  M  and  thence  to  G,  a  portion  continuing  to  H;  that  which  does 
not  pass  from  the  glass  at  G  is  reflected  to  N,  thence  to  I,  and  a  part 
contmues  to  J,  etc.  This  continues  until  the  light  can  no  longer  be 
perceived  as  the  intensity  is  reduced  at  each  reflection.  An  image  is 
created  by  the  points  of  reflection  C  K  E  M  G  N  I.  The  further  away 
from  the  first  point  of  reflection  the  fainter  the  image  becomes.  As 
E  and  K  are  in  the  same  plane  the  images  they  create  are  seen  as  one, 
being  superimposed,  the  same  is  true  of  G  M  and  I  N.  The  above 
phenomena  is  termed  multiple  reflection,  and  shows  that  even  glass  does 
not  transmit  all  the  light  that  strikes  it,  but  reflects  a  portion. 


Hold  a  lighted  candle  near  a  thick  glass  mirror,  look  at  its  image 
reflected  in  the  mirror  in  a  line  perpendicular  to  the  surface  of  the 
mirror,  but  one  image  will  be  seen  with  a  faint  ghost  of  another  back 
of  it.  Now  move  to  a  position  so  that  the  visual  line  strikes  the  sur- 
face of  the  mirror  obliquely  and  several  images  of  the  flame  will  ap- 
pear. The  more  oblique  the  angle  the  greater  number  of  images  will 
be  seen.  The  reflections  from  the  surfaces  of  glass  account  for  the 
annoying  phenomena  that  glass  wearers  sometimes  complain  of  when 
they  first  attempt  to  wear  them. 

Figure  13  represents  a  sphere  S,  the  centre  of  which  is  at  C.  Any 
straight  line  drawn  from  C  to  the  circumference  will  be  a  radius  of 
the  sphere  and  therefore  a  perpendicular  to  the  circumference  at  the 
point   of  incidence.        Let  A  B  represent  a  concave   mirror;  being  a 


Figure  13. 

A  concave  mirror  is  a  section  of  a  sphere.       The  aperture    A  B;    centre  of  curvature,   C; 
vertex,  D;  radius,  A  C;  principle  axis,  D  C;  focus,  P;  focal  length,  D  P. 

section  of  S  its  centre  of  curvature  will  be  at  C,  the  geometric  centre 
of  the  sphere.  A  point  D,  located  half  way  between  A  and  B  upon  the 
surface  of  the  mirror,  is  called  the  vertex  of  the  mirror,  and  a  straight 
line  drawn  through  the  centre  of  curvature  and  the  vertex  indicates 
the  principle  axis  of  the  mirror.  The  aperture  of  the  mirror  is  the  dis- 
tance between  A  and  B. 

If  light  be  placed  at   the  centre  of  a  concave  mirror,  it  will  be 
reflected  from  all  points  upon   the   surface  of  the  mirror  back  to  its 


i8  O  C   U   L  A   R         K   K   F    K   A  C  T   I   ()  N. 

source;  the  path  of  each  ray  will  be  a  radius  of  the  mirror  and  will  be 
perpendicular  to  the  small  plane  at  the  point  of  incidence;  thus,  the 
incident  and  reflected  rays  traverse  the  same  path.  Any  ray  passing 
through  the  centre  of  curvature  of  a  concave  mirror  and  incident  at 
any  point  upon  the  mirror  other  than  the  vertex,  is  reflected  to  its 
source  and  its  path  is  said  to  be  a  secondary  axis  of  the  mirror. 

Figure  14  represents  a  concavr  mirror  A  B  ;  from  the  points  E  and 
F  located  at  equal  distances  from  the  vertex  upon  A  B,  draw  the  radii 
and  locate  the  centre  C  and  the  principle  axis  D  C.  Suppose  parallel 
rays  strike  the  mirror,  one  ray  traversing  the  principle  axis,  the  ray 
R,  incident  at  E,  and  S  at  F,  form  the  angles  of  incidence  R  E  C  and 
S  F  C;  constructing  the  angles  of  reflection  CEP  and  C  F  P,  it  is 
found  that  the  reflected  rays  meet  at  a  point  P  on  the   principle  axis 


lei  rays  by 


which  is  called  \.h&  principle  focus  of  the  mirror;  it  is  located  half  way 
between  the  centre  of  curvature  and  the  vertex.  By  this  it  is  proved 
that  any  ray  from  an  object,  parallel  to  the  principle  axis  of  a  concave 
mirror,  by  reflection  passes  through  the  principle  focus.  The  distance 
between  the  vertex  and  the  principle  focus  is  the  measure  of  ihe  focal 
length  of  the  mirror.  A  concave  mirror  renders  parallel  rays  con- 
vergent, and  light  situated  at  the  focal  point  is  projected  parallel  by 
reflection.  The  focus  then  is  a  point  at  wliich  light  rays  that  diverge 
from  one  point  meet  again  after  reflection. 

Figure  15  represents  a  concave  mirror  A  B ;  the  light  (radiant 
point)  is  situated  at  the  point  G  upon  the  principle  axis  which  is  be- 
yond the  centre  of  curvature  C;  from  the  points  E  and  F  located  upon 
A  1^,  equally  distant  from  the  vertex  1),  construct   the   angle  of   inci- 


dence  G  E  C  and  G  F  C,  for  the  rays  G  E  and  G  F,  and  the  angles  of 
reflection  C  E  H  and  C  F  H.  The  rays  will  be  found  to  focus  at  H  ; 
by  the  same  construction,  if  the  light  were  situated  at  H  the  rays 
would  be  brought  to  a  focus  at  G.  The  points  G  and  H  thus  bear  a 
definite  relation  to  each  other.  Light  situated  at  either  is  reflected  to 
the  other  and  these  points  are  called  conjugate  foci.  The  conjugate 
foci  of  rays  reflected  from  an  object  by  a  concave  mirror,  are  upon  the 
same  side  of  the  mirror,  when  the  object  is  situated  beyond  the  focus; 
either  may  be  taken  as  the  location  of  the  radiant  point  and  their 
positions  are  reversible. 

Qoncavc  mirrors  reduce  tlic  divergency  and  increase  the  convergence  of 
incident  rays.  The  images  ci-eated  by  concave  mirrors  vary  with  the 
position  of  the  object  reflected. 


elleclion  of  divergent  rays  by 


//  the  object  t'c  situated  beyond  the  centre  of  curvature,  the  image  is  real , 
smaller  than  the  object,  inverted,  and  located  betiveen  the  principle  focus  and 
the  centre  of  curvature. 

If  the  object  he  situated  between  the  principle  focus  and  the  centre  of  curva- 
ture, the '  image  is  real,  magnified,  inverted,  and  located  beyond  the  centre  of 
curvature. 

If  the  object  be  situated  between  the  principle  focus  and  the  mirror,  the 
image  is  -virtual,  not  invert,  d.  ma^^uilied.  and  located  I'cliiud  the  mirror. 

If  the  object  be  .utuatcd  cxactlv  at  the  centre  of  curvature  no  image 
is  foniied.  as  the  object  and  the  image  arc  located  at  the  same  foint. 

Take  a  bright  new  spoon  and  using  the  bowl  as  a  concave  mirror, 
reflect  a  pin  in  it;  with  the  pin  in  contact  with  the  surface  it  appears 
erect  and  slightly  magnified,  withdraw  it  slowly,  the  image  remains 
erect  and  the  magnification  increases  until  the  image  blurs  and  finally 
disappears.     This  indicates  that  the  pin  is  located  at  the  centre  of  cur- 


20  O  C  U  L  A   R         R   1-:   F   R  A  C  T   I  O   X. 

vature  of  the  bowl  of  the  spoon.  Withdrawn  still  further  from  the 
surface  of  the  bowl,  the  image  reappears  but  is  inverted  and  smaller 
than  the  pin. 

Figure  i6  represents  a  convex  mirror  A  B;  its  centre  of  curva- 
ture is  at  C  which  is  behind  the  surface  of  reflection.  Rays  from  G 
to  E,  and  from  G  to  F  are  reflected  to  L  and  M;  C  H  and  C  K  are 
perpendiculars  to  A  B  at  the  points  of  incidence  E  and  F;  G  E  H  and 
G  F  K  are  the  angles  of  incidence,  L  E  H  and  M  F  K  the  angles  of 
reflection;  hence,  E  L  and  F  M  indicate  the  paths  of  G  E  and  G  F 
after  reflection. 

Convex  mirrors  increase  the  divergence  of  incident  rays,  render 
parallel  incident  rays  divergent,  and  reduce  tJic  convergence  of  incident 
rays;  they  may  reflect  convergent  rays  as  parallel  or  even  divergent. 


is,  c.  D. 

The  image  formed  by  a  convex  mirror  is  smaller  than  the  object,  is 
erect,  -virtual  and  situated  behind  the  mirror. 

An  image  of  anything  is  a  copy,  reproduction  or  counterpart  of  it 
An  optical  image  is  an  appearance  of  an  ob/cct  created  by  the  projection 
of  a  single  ray  from  every  point  upon  an  cb/ect  tin-ough  nii  infinitelv 
small  apertui-c'upon  a  screen:  also  created  by  I  be  re/ci  I  ion  of  incident 
rays  upon  a  mirror  from  every  point  upon  the  object,  or  their  refraction 
by  some  medium. 

There  are  two  kinds  of  optical  images,  real  and  \\r\.i\&\;  a.  real 
m«_o-^  is  one  that  can  be  received  upon  a  screen ;  it  is  created  when 
the  conjugate  foci  of  rays  are  upon  the  same  side  of  a  mirror,  also 
created  by  rays  passing  through  an  aperture  A  virtual  image  is  one 
that  cannot  be  projected  and  received  upon  a  screen,  but  reaches  the 
eye  by  reflection  and  the   rays   form  a  real    image    upon    the    retina. 


The  formation  of  images  by  a  lens  will  be  taken  up  under  the  subject 
of  lenses. 

Figure  17  represents  a  lighted  candle  placed  before  a  thin  opaque 
plate  P  of  say,  tin,  having  a  very  small  aperture  at  A  A;  the  screen  of 
white  cardboard  I  is  placed  back  of  the  plate  to  receive  the  image. 
Rays  R  from  all  points  of  the  candle  meet  the  plate  P  and  are  inter- 
cepted by  it,  only  those  reaching  A  A  pass  through  and  are  received  by 
the  screen  I;  if  A  A  were  small  enough  only  one  ray  from  each  point 
would  reach  I.  As  the  paths  of  the  rays  are  straight,  a  ray  from  each 
of  the  points  A,  B  and  C  reach  the  screen  at  the  points  A',  B'  and  C ; 
the  same  is  true  of  all  rays  forming  the  image  and  this  shows  why  the 
images  formed  by  apertures  are  inverted.  If  the  distance  of  the 
screen  from  the  aperture  is  equal  to  the  distance  of  the  candle  from 
the  aperture,  the  image  will  be  the  same  size  as  the  candle;  if  further 
away,  say  at  I',  the  image  A"  B"  C"  will  be  larger  than  the  object; 
the  nearer  the  screen  is  brought  to  the  aperture  the  smaller  and 
brighter  will  be  the  image.  If  the  aperture  is  made  through  a  thick 
plate  the  image   formed  will  be  poor.     To  obtain  a  clear  cut  image  it 


Figure  17. 

Formation  of  image  by  an  aperl 


is  necessary  to  have  the  smallest  possible  aperture  in  the  thinnest 
possible  plate.  A  camera  can  be  constructed  upon  this  principle  and 
photographs  made  without  the  use  of  a  lens,  which  in  point  of  detail 
are  superior  to  those  made  with  a  lens.  The  greatest  drawback  to 
such  pictures  is  the  time  required  for  the  exposure  (.'ue  to  the  small 
amount  of  the  light  projected  upon  the  plate.     Any  number  of  aper- 


O  C   U  L  A 


K    E   1-  R   A  C  T  I 


tures  can  be  used  in  the  expsriment  illustrated  by  figure  17,  and  each 
will  create  an  imag-e  which  will  be  distinct  so  long  as  it  is  not  over- 
lapped by  the  image  from  another  aperture;  when  the  apertures  are 
so  close  together  that  the  images  they  create  overlap,  the  result  is  illu- 
mination and  no  formation  of  distinct  images. 

Figure  18  represents  a  plane  mirror  A  B,  to  the  eye  placed  at  E 
the  image  of  the  candle  C  appears  by  reflection  at  C,  which  is  the 
same  size  and  shape,  in  other  words,  an  identical  reproduction  of  C, 
and  located  behind  the  mirror  the  same  distance  that  the  candle  is  in 
front  of  it. 


%' 


Figure 


To  locate  the  position  of  an  image  created  by  a  concave  mirror 
let  figure  ig  represent  a  concave  mirror  A  B;  its  centre  of  curvature 
at  C;  the  principle  focus  at  P;  the  object  being  located  at  L  M,  beyond 
the  centre  of  curvature.  Draw  the  principle  a.xis  C  D  and  parallel  to 
it  draw  the  incident  ray  L  E,  which  is  reflected  through  the  principle 
focus;  another  ray  from  the  same  point  L  through  the  centre  of  cur- 
vature is  incident  at  H  and  on  reflection  meets  the  reflected  ray  E  P 
at  L';  this  is  the  conjugate  foci  of  all  rays  from  the  point  L  and  at  L'  is 
formed  the  image  of  this  point.  In  the  same  way  locate  the  image  of 
M  at   M'    and  the    points    between  L  and  M  will    be    imaged  between 


L'  and  M'.  This  diagram  may  be  reversed  to  show  L'  M'  as  the  ob- 
ject and  L  M  as  the  image.  In  either  case  the  images  are  real,  being 
formed  by  rays  that  actually  meet  after  reflection. 


Figure 


I  i  mage  by  a  c< 
object,   L  M;  imaije. 


idary  ax 


the  object  being  situated  beyond  tlie  ce 
;  centre  of  curvature,  C;  principle  foe 
■s,  L  H  and  M  G. 


Figure  20  represents  an  object  L  M  so  placed  with  regard  to  the 
mirror  that  no  ray  passes  from  it  along  the  principle  axis.  To  locate 
the  image  in  such  cases  draw  the  path  of  a  ray  from  the  point  L  par- 
allel   to    the    principle   axis  and    incident   at    F,  from  F  it  is  reflected 


Position  of  image  of  obj 


through  the  principle  focus;  another  ray  from  the  same  point  L  form- 
ing a  secondary  axis  L  E.  The  conjugate  foci  of  E  L  and  F  P  lo- 
cates the  image  of  the  point  L  at  L';  in  the  same  manner  locate  the 
image  of  M  at  M',  etc.  When  the  object  lies  wholly  to  one  side  of  the 
principle  axis  the  image  is  upon  the  other. 


O  C   U   L  A  K 


R  E  F  R  A   C  T  I  O  N. 


In  figure  21  the  object  L  M  is  situated  between  the  principle 
focus  P  and  the  vertex  D  An  incident  ray  L  E  parallel  to  the 
principle  axis  C  D  is  reflected  through  the  principle  focus  P;  a  second- 
ary axis  C  L  meets  A  B  at  G  and  a  ray  from  L  to  G  is  reflected 
through  C;  the  reflected  rays  G  C  and  E  P  are  divergent  and,  there- 
fore, cannot  meet;  they  have  but  a  virtual  focus  which  is  located  by 
extending  them  back  of  the  mirror  where  they  meet  at  the  point  L'; 
the  point  M'  is  found  in  the  same  way,  and  L'  M'  represents  the  vir- 
tual image  of  L  M. 

Figure  22  shows  at  a  glance  the  characteristics  of  images  formed 
of  objects  in  different  positions  with  regard  to  a  concave  mirror;  the 
dotted  lines  connect  each  object  and  its  image.     The-  image  of  L  is 


elween  principle 
:  ol)jecl,  L  M;  image  L  M';  principle  focus,  P. 

at  L',  is  inverted,  real  and  magnified;  the  image  of  L'  is  at  L,  is  in- 
verted, real  and  smaller,  the  image  of  N  is  at  N',  is  erect,  virtual  and 
slightly  magnified;  while  the  image  of  M  is  at  M',  is  erect,  virtual  and 
greatly  magnified.  The  centre  of  curvature  is  represented  at  C,  the 
principal  focus  at  P,  and  the  mirror  at  A  B. 

Figure  23  illustrates  the  formation  of  the  image  by  a  convex 
mirror.  The  object  is  at  L  M,  the  mirror  is  A  B.  To  locate  the  im- 
age of  the  point  L,  draw  the  path  of  a  ray  from  L  through  C;  another 
from  L  parallel  to  C  D,  construct  the  angles  of  incidence  L  F  F'  and 
the  angle  of  reflection  K  F  F';  by  extending  K  F  back  of  the  mirror 
as  a  straight  line,  it  meets  L  C  at  L'.  Anutner  ray  from  L  to  E  is 
reflected  to  H,  L  E  E'  being  equal  to  H  E  E';  extending  fl  E  back 
of  the  mirror  as  a  straight  line  it  also  passes  through  L',  which  is, 
therefore,  the  virtual  focus  for  all  rays  from  the  point  L.  In  the 
same  manner  locate    the    focus  of    M  at  M';  thus,  L'  M'  is  the  virtual 


image  of  L  M.  By  reversal,  figure  21  shows  the  construction  of  the 
image  created  by  a  convex  mirror  taking  L'  M'  as  the  object,  L  M 
will  be  the  image. 


Figur 


ng  kind  an 
positii 


piisition   of  images  foinied  by 
IS.     Dotted  lines  join  object  ant 


Considerable  space  has  been  devoted  to  the  subject  of  reflection 
by  mirrors  and  this  indicates  its  importance. 

The  student  is  urged  not  to  pass  beyond  this  subject  until  he  has 
thoroughly  mastered    it,    practising    the    formation  of  images  by  dia- 


Figure  23. 

mirror.      The  object  L  M  ; 
:,  C;  virtual  focus,  P. 


grams  drawn  by  himself  ;    no    matter   how   poor  a   draughtsman    he 
may  be,  the  practice  will  be  valuable.     The  subject    may  seem   com- 


c  u 


R   E   F 


ACTION 


plicated  at  first,  but  there  are  only  a  few  important  points  to  under- 
stand, and  it  becomes    easy. 

As  the  retinoscope  is  but  a  plane,  or  concave  mirror,  by  which 
light  is  reflected  into  the  eye,  causing  certain  phenomena  by  which 
the  refraction  of  the  eye  is  estimated,  it  can  readily  be  appreciated  that 
the  laws  of  reflection  by  mirrors  should  be  thoroughly  understood. 

iVIirrors  are  surfaces  that  reflect  light  in  definite  directions,  as 
we  have  seen,  but  every  body  reflects  light;  rays  that  are  incident 
upin  a  surface,  that  is  irregular,  are  not  regularly  reflected,  but  are 
reflected  in  all  directions  or  scattered.  Under  such  conditions  light 
is  said  to  be  diffused  a.nA  no  image  is  created  by  the  reflecting  surface. 

The  beam  of  light  composed  of  the  rays  R,  tigure  24,  approach 
the  surface  of  C  D  in  a  definite  direction  and  are  reflected;  as 
the  surface  C  D  is  irregalar  or  roughened,  all  its  points  do  not  lie  in 
the    same  plane  and  the  angles  of    incidence  must  vary  for  each   ray; 


Figure  24. 
DifTusiun  of  light  by  reflection. 

the  angles  of  reflection  are  also  different  and  the  reflected  rays  are 
scattered  in  all  directions  creating  diffused  light. 

It  is  by  diffused  light  that  most  objects  that  we  see  are  rendered 
visible.  They  are  said  to  be  illuminated  and  may  be  seen  from  any 
direction,  as  they  receive  and  reflect  light  from  all  directions 

Incident  rays  upon  the  surface  bounding  two  media  of  dififerent 
density  are  divided  at  the  surface,  a  portion  we  know  is  reflected, 
the  remainder  is  transmitted  ;  the  manner  of  transmission  varies  and  is 
dependent  upon  given  conditions.  There  are  certain  laws  with  re- 
gard to  the  incident  and  reflected  rays  that  are  similar  to  those  gov- 
erning the  transmitted  ray  and  this  simplifies  the  study.  The  path 
of  the  incident  ray  that  is  perpendicular  forms  a  straight  line  with  the 
path  of   the  reflected  ray;  so,  too,  the  path  of  the  incident  ray  that    is 


perpendicular  forms  a  straight  line  with  the  path  of  the  transpiitted 
ray.  The  incident  ray  that  is  not  perpendicular  forms  an  angle  with 
the  perpendicular  and  also  with  the  transmitted  ray;  this  is  the  foun- 
dati<m  for  the  following  law: 

The  path  of  li,^ht  niys  fassiu-,^  obUqitcIy  from  one  incdiiin,  to  an- 
other of  different  denuty  ix  broken  at  the  surfaee  boundini::  the  uiedia; 
this  is  termed  the  refraelion  of  Iio;ht. 

If  the  p-ith  of  rays  passing  from  one  medium  to  another  of  differ- 
ent density  strikes  the  surface  bounding  the  media  perpendicularly, 
they  arc  not  refracted;  the  path  of  the  rays  in  the  second  medium  will 
he  a  coniinuation  in  a  straight  line  of  their  path  in  the  first.  If  thev 
are  not  perpendicular  they  are  refi'acted  and  the  paths  in  the  first  and 


i^5 


Figure  25. 

ay,   L;   incident  point,    M;   boundi 
C  D;refracle(l  ray,  M  O. 


A   B;  perpend icula 


second  media  will  not  be  a  straight  line,  for  they  will  fnnn  an  angle 
whose  vertex  is  at  the  bounding  stirface;  refraction  then  /j  a  breaking 
of  the  path  of  the  light  ray. 

Figure  25  represents  a  ray  of  light  from  L  passing  through  a 
small  aperture  in  the  side  of  a  vessel  and  incident  at  M  upon  the  sur- 
face A  B  of  the  water,  C  D  is  the  perpendicular  to  A  B  at  the  point 
of  incidence  M.  It  will  be  found  that  M  O  will  represent  the  path 
of  the  light  through  the  water  instead  of  M  N,  the  original  direction 
of  L  being  changed  at  M.  This  indicates  the  point  of  refraction  for 
the  rays  from  L  upon  the  surface  of  the  water.  If  the  radiant  ])oint 
were  situated  at  C  and  rays  followed  the  path  C  M,  they  would  be 
transmitted  to  the  point  D;  the  path  of  the  incident  rays  C  M  and 
that  of  the  transmitted  rays  M  D  would  thus  form  an  unbroken 
straight  line,  for  C  M  is  perpendicular  to  A  B,  while  L  M  is  not. 


28 


OCULAR 


REFRACTION. 


Tlic-siriin-  rays  -k' ill  he  refracted  as  often  as  they  may  meet  another 
medium  of  different  (/(V/.wVj',  according  to  the  law  of  refraction  ;  this 
fact  is  made  use  of  in  various  ways  to  correct  certain  faults  of  refrac- 
tive metlia  which  will  be  explained  later  on. 

l,et  figure  26  represent  a  vessel  partly  filled  with  water,  A  B  in- 
dicating the  surface.  The  ray  from  L  passes  to  M  and  undergoes  re- 
fraction through  the  water  to  O  instead  of  continuing  on  to  N.  A'  B' 
indicates  the  surface  of  a  block  of  glass  G  upon  the  bottom  of  the  ves- 
sel. As  the  density  of  glass  and  water  is  different  M  O  undergoes 
further  refraction  at  O  and  strikes  the  bottom  of  the  vessel  at  O'  in- 
stead of  at  P.  If  the  path  of  the  ray  were  C  M,  it  would  meet  A'  B' 
at  D,  and  if  A'  B'  were  parallel  to  A  B,  M  D  would  pass  to  E  and 
the  points  CM  D  E  would  be  found  to  be  in  the  same  line. 


A         ^\   M ^ B 


Figure  26. 

Refraction  of  ray  L  al  surface  A  B  and  again  at  A'  B'. 

A  pencil  placed  obliquely  in  a  glass  of  water  appears  broken 
where  it  enters  the  water;  an  oar  placed  over  the  side  of  a  boat  into 
the  stream  appears  to  be  bent  at  the  surface;  the  part  immersed  ap- 
pears shortened  and  bent  upward.  One  of  the  effects  of  refraction  is 
to  create  a  false  idea  of  depth;  objects  upon  the  bottom  of  a  clear 
stream  appear  much  nearer  t  e  surface  than  they  actually  are,  because 
the  water  is  of  greater  depth  than  it  appears  to  be;  the  rays  of  light 
reaching  the  eye  from  the  objects  upon  the  bottom  undergo  refrac- 
tion at  the  surface  of  the  water  on  emerging  into  the  air. 

Tlie  direction  of  the  light  rays  from  the  point  of  refraction, 
through  the  second  medium  is  in  a  straight  line,  conformiiig  to  the  lavv 
that  light  always  travels  in  a  straight  fine.  It  is  true  that  the  direc- 
tion of  the   ray  is  changed  by  refraction,   but  it   is  due  to  a  sharply 


L  I  G  H  T. 


29 


defined  break  at  the  point  of  incidence;  after  refraction  its  path  is 
again  in  a  straight  line.  In  defining  refraction  the  term  breaking  is 
used  rather  than  l>i-/iif//ig  as  it  does  not  convey  the  idea  of  a  curve. 

It  is  well  known  that  a  person  can  run  faster  on  land  than  if  they 
attempt  to  run  in  water  up  to  their  waist.  The  water  is  of  greater 
density  than  the  air  and  impedes  one's  progress.  The  light  waves 
experience  a  similar  impediment  to  their  progress,  which  is  retarded 
if  they  pass  from  a  rare  to  a  dense  medium;  accelerated  if  they  pass 
from  a  dense  into  a  rare  medium. 

Refraction  is  due  to  the  fact  that  the  veloeity  of  light  is  /ess  in  a 
dense  than  in  a  rare  iiiediniii 


Diagra 


Figure  27  explains  how  refraction  occurs;  G  represents  a  piece 
of  glass  whor>e  sides  are  parallel ;  the  source  of  illumination  is  L. 
From  L  the  light  proceeds  to  M  along  the  line  L  M,  the  front  of  the 
light  wave  is  always  perpendicular  to  the  line  of  propagation  at  the 
point  of  intersection,  and  we  can  represent  the  light  waves  by  a  series 
of  parallel  lines  W  at  right  angles  to  L  M.  Passing  through  the  air 
from  L  to  M  every  portion  of  the  wave  moves  with  equal  velocity, 
the  density  of  the  air  being  uniform.  On  approaching  the  glass  the 
point  A  of  each  wave  enters  the  glass  before  the  point  B;  owing  to 
the  greater  density  of  the  glass  than  air  the  progress  of  A  is  retarded 
while  that  of  B  is  not,  and  while  the  point  A  moves  to  A',  B  moves  to 


30  O  C  I'   L  A  R         R  E  F  R  A  C  T  I  O  N. 

B'  in  the  s^ame  time.  This  gives  a  new  direction  to  the  waves,  and 
as  the  line  of  propagation  is  at  right  angles  to  the  waves,  by  drawing 
a  line  from  the  point  of  incidence  M,  perpendicular  to  the  parallel 
lines  A'  B',  the  direction  the  rays  will  take  through  the  glass  will  be 
obtained  The  point  where  the  rays  meet  the  second  surface  of  the 
glass  will  be  located  at  N.  On  emerging  from  the  glass  at  N  the 
point  C  of  each  wave  leaves  the  glass  before  the  point  D,  and  air 
being  less  dense  the  velocity  of  C  is  increased  while  that  of  D  is  un 
changed;  hence,  in  the  same  time  that  D  moves  to  D',  C  moves  to  C. 
Another  change  of  direction  is  given  to  the  wave  at  the  point  of 
emergence  N,  and  to  find  the  new  direction  the  wave  will  take  from 
the  point  N,  draw  a  line  perpendicular  to  the  lines  C  D',  which  will 
indicate  the  path  of  the  emergent  rays  from  N  to  O.  When  a  file  of 
soldiers  make  a  turn  from  their  line  of  march  they  "execute  a  wheel' 


Figure  28. 

Refraction  by  glass  with  parallel  surfaces. 

in  order  to  keep  their  alignment,  those  upon  the  pivotal  end  marking 
time  while  those  upon  ihe  other  end  quiclcen  their  pace;  this  is  similar 
to  what  occurs  to  the  light  rays  upon  refraction,  they  execute  a  kind 
of  wheel  at  the  point  of  incidence. 

The  surfaces  of  the  glass,  figure  27,  are  parallel  planes,  and  the 
lines  N  O  and  L  M,  indicating  the  paths  of  the  light  as  it  enters  and 
leaves  the  glass,  are  parallel. 

Figure  28  represents  a  thick  strip  of  plate  glass  held  horizontally 
across  a  paper  upon  which  a  perpendicular  black  line  Wis  drawn; 
when  the  line  is  viewed  obliquely  through  the  glass,  it  appears  broken 
at  the  edges  of  the  glass;  that  portion  seen  through  the  glass  is  dis- 
placed to  one  side  or  the  other  as  the  glass  is  inclined  toward  the  sur- 
face of  the    paper;  if  the  glass  is  held  so  that  its  surface  is  parallel  to 


the  plane  of  the  paper,  and  the  eye  be  placed  so  that  the  line  of  vision 
is  perpendicular  to  the  surfaces,  the  line  drawn  upon  the  paper  will 
not  be  broken. 

The  incident  ray  that  is  not  refracted  must  be  perpendicular  to 
the  surfaces  of  the  medium  and  they  must,  therefore,  be  parallel  to 
each  other. 


G 

s  I I  n 


Diagr 


Figure  2g. 

hat  refrnclion  does  not  £ 


Figure  29  explains  how  light  can  be  transmitted  wthout  refrac- 
tion. The  surfaces  A  B  and  C  D  of  the  glass  G  are  parallel,  the  in- 
cident ray  R  is  perpendicular  at  the  point  E ;  as  the  waves  are  pierced 
at  right  angles  by  the  line  of  propagation  they  must  be  parallel  to 
A  B  and  C    D.      Upon  approaching  the  glass  all  points  on  the  wave 


enter  the  glass  at  the  same  time  and  are  equally  retarded,  so  that  the 
direction  of  the  wave  is  unchanged;  leaving  the  glass  all  points 
emerge  at  the  same  time  and  are  equally  accelerated,  so  that  there  is 
no  refraction  and  the  path  from  R  to  S  is  a  straight  line. 


32 


O  C  U  L  A 


E  F  R  A  C  T  I  O  N. 


Light  IS  alivays  ri'/ractcd  when  transmitted  liy  a  nicdiiiin  ivhosc 
bounding  surfaces  are  not  parallel;  no  matter  wr.at  the  angle  of  inci- 
dence the  ray  cannot  be  perpendicular  to  both  surfaces  and  must  be 
refracted  by  at  least  one. 

Figure  30  represents  a  piece  of  glass  whose  surfaces  E  F  and 
H  K  are  mt  parallel.  The  incident  ray  from  A  is  perpendicular  to 
E  F  at  B  and  passes  to  C  without  refraction;  at  C  it  is  not  perpen- 
dicular to  H  K  and  undergoes  refraction.  Some  rays  not  perpen- 
dicular to  E  F  may  also  meet  H  K  obliquely  and  will  be  refracted  by 
both  surfaces. 


Diagr: 


Figure  31. 

lirection  tlie  refracted  ) 


ill  take. 


'to  a  dense  niediuiii  and  refracted,  is 
ion  from  the  point  of  incidence  into 
into  a  rare  tnediuni  and  refracted  is 
iwn  from    the  point  of  incidence  into 


Light  passing  from  a  rare  i. 
bent  toieard  the  perpendicular  dr, 
the  scccnd  medium;  from  a  dense 
bent  toiuard  the pet'pendicular  dr 
the  second  medium. 

In  figure  31  A  B  C  D  represents  a  rectangular  vessel  so  placed  in 
a  darkened  room  that  a  ray  of  light  that  is  admitted  through  a  small 
aperture,  falls  in  the  direction  indicated  by  the  line  L  A,  over  the 
edge  of  the  vessel;  it  will  thus  strike  the  bottom  obliquely,  its  path 
being  LAM.  Now,  without  moving  the  vessel,  fill  it  with  water  so 
that  the  surface  will  ba  indicated  by  A  D;  the  light  will  now  strike 
at  a  point  between  jI  and  B  which  we  will  indicate  as  N,  showing 
that  its  path  is  now  LAN.  On  entering  the  denser  medium,  water, 
it  is  refracted  toward  the  perpendicular  drawn  from  the  point  of  in- 
cidence A  into  the  water,    which  will  be  A  B.      Empty  the    vessel  of 


LIGHT.  33 

the  water  and  place  it  in  its  former  position ;  admit  ample  light  to 
the  room,  and  if  a  card  perforated  with  a  small  round  hole  be  placed 
at  L,  on  looking  through  this  hole  in  the  direction  L  A  the  point  M 
on  the  bottom  of  the  vessel  will  be  seen.  Have  some  one  place  a 
coin  at  this  point  and  continue  looking  in  this  same  direction;  if  the 
vessel  is  now  filled  with  water  to  A  D  the  coin  will  disappear  from 
view  at  L.      At  the  point  N  now  seen  upon  the  bottom,  have  another 


Figure  32. 


Melhod  of  deter 


1  of  index  of  refrac 


Incident  ray,  L  P;  refracted  lay,  P  L  . 


coin  of  different  denomination  placed  so  as  to  differentiate  between 
the  two.  The  coins  are  seen  by  the  light  they  project  to  the  eye. 
When  the  vessel  was  empty  the  light  rays  from  M  reached  the  eye  at 
L  along  the  straight  line  M  A  L,  for  they  traversed  only  air  between 
M  and  L ;  with  water  to  the  line  A  D  and  the  eye  at  L,  the  coin  at  N  is 
seen,  showing  that  the  rays  from  N  reach  the  eye  along  the  path 
N  A  L  which  is  not  straight.  Were  N  A  prolonged  as  a  straight  line 
it  would  reach  the  point  F,  which  is  nearer  the  perpendicular  A  E 
than  L ;  rays  following  the  path  N  A  on  emerging  from  water  into  air, 
a  rare  medium,  are  bent  away  from  the  perpendicular  A  E. 

Tlie  deviation  of  light  i^<lieii  refracted  varies  icitli  the  angle  of  inci- 
dence and  the  density  of  the  refracting  inediniu.  The  angle  of  refrac- 
tion increases  as  the  angle  of  incidence  is  increased  and  becomes 
smaller  as  the  angle  of  incidence   is  reduced  until  at  zero  there  is  no 


34  OCULAR         K   E  F   K  A  C  T   I  O  X. 

deviation,  (see  figure  29)  the  incident  ray  being  perpendicular.  Of 
two  media  the  angles  of  incidence  being  the  same,  that  having  the 
greater  density  will  have  the  greater  angle  of  refraction  as  it  offers  a 
greater  resistance  to  the  passage  of  the  light  waves.      (See  Fig.  27  ) 

It  has  been  found  that  the  measure  of  the  angles  of  incidence  and 
refraction  bear  a  certain  ratio  to  each  other  for  any  two  given  media; 
it  is  called  the  index  of  refraction. 

To  find  the  index  of  refraction  for  any  two  media,  the  angles  o 
incidence  and  refraction  being  known,  draw  a  circle,  figure  32,  with  the 
point  of  incidence  P  as  its  centre,  C  D  is  the  surface  separating  the 
media;  draw  A  B  perpendicular  to  C  D  through  P.  The  incident  ray 
L  cuts  the  circle  at  E  and  the  refracted  ray  L'  at  H,  from  E  drop  a 
perpendicular  E  F  to  the  line  A  B  and  from  H  another  perpendicular 
H  G  to  A  B.  Suppose  that  the  line  E  F  is  6/10  the  length  of  the  ra- 
dius E  P,  6/10  is  called  the  sine  of  the  angle  EPA,  which  is  the  angle 
of  incidence.  Suppose  that  H  G  is  4/10  the  length  of  the  radius  H  P, 
4/10  is  the  sine  of  the  angle  ot  refraction  H  P  B.  The  sines  of  the  two 
angles  are  to  each  other  as  6/10  :  4/10,  or  6  :  4  which  equals  1.5;  if  the 
media  taken  in  this  example  were  air  and  glass, the  index  of  refraction 
given  would  be  correct,  the  index  of  the  refraction  of  glass  compared 
with  air,  the  optical  unit  is  about  1.5 

The  index  of  refraction  is  the  ratio  of  the  sines  of  the  angles  of 
ineidenee  and  re  fraction,  for  a  ray  of  light  passing  from  one  inediuin 
into  another . 

When  we  speak  of  the  inde.x  of  refraction  of  any  medium  it  is 
usual  to  consider  its  refractive  value  compared  to  that  of  air. 

The  index  of  refraction  for  any  two  media  indicates  the  relation 
that  the  velocity  of  light  in  one  medium  bears  to  its  velocity  in  the 
other. 

We  know  that  the  degree  of  refraction  that  a  ray  undergoes  is 
dependent  upon  the  angle  of  incidence;  the  incident  ray  being  perpen- 
dicular, or  normal  to  the  surface  there  is  no  refraction;  as  the  angle  of 
incidence  increases,  the  angle  of  refraction  increases  rapidly  until 
finally  it  forms  90  degrees  with  the  perpendicular  and  such  an  angle  of 
incidence  is  called  the  critical  angle;  if  the  angle  of  incidence  be  still 
further  increased,  the  angle  of  refraction  becomes  greater  than  90  de- 
grees, and  no  light  passes  into  the  second  medium,  because  on  meet- 
ing the  surface  bounding  the  media  it  is  refracted,  or  really  reflected, 
back  into  the  same  medium;  thus,  whenever  the  incident  ray  from  a 
dense  into  a  rarer  medium  meets  the  surface  bounding  the  media  at  an 
angle  greater  than  the  critical  angle  it  is  totally  rejleeted. 


Figure  33  represents  a  vessel  filled  with  water  to  the  line  A  B.  A 
ray  of  light  from  D  to  C  is  normal  to  A  B  and  is  not  refracted  but 
passes  to  D';  the  ray  L  meets  A  B  at  C  forming  the  angle  of  incidence 
LCD  and  is  refracted  in  the  direction  I.';  another  ray  M  forms  the 
angle  of  incidence  M  C  D  and  is  refracted  in  the  direction  M';  the  ray 
N  forms  the  angle  of  incidence  N  C  D  and  its  angle  of  refraction  is 
D'  C  N'  which  is  90  degrees,  N'  being  parallel  to  the  surface  A  B,  N  C  D 
is  then  the  critical  angle;  the  ray  O  forms  the  angle  of  incidence  O  C 
D  which  is  greater  than  the  critical  angle  and  at  C  the  ray  O  is  bent  in 
the  direction  O'.  it  is  therefore  not  transmitted  into  the  second  medium 
but  reflected.  To  simplify  the  tracing  of  the  path  of  each  ray  in  the 
figure  (33)  a  different  form  of  broken,  dotted  and  unbroken  line  is  used 
for  each. 


0^^  \ 

N'  ^\^  C 


Figure  33. 

s,  D,  L,  M,  N.  O;  refracted 
critical  angle,  N  CD. 


ays,  LM'N;;    reflected   ray    O, 


If  a  coin  be  placed  in  a  glass  filled  with  water  and  the  glass  held 
so  that  in  looking  upward  at  an  angle  upon  the  surface  of  the  water, 
the  coin  will  be  seen  mirrored  upon  the  surface.  This  property  of 
total  reriection  is  the  basis  for  the  angles  of  the  facets  upon  gems,  by 
total  reflection  their  brilliancy  is  obtained.  The  reason  that  we  have 
daylight  after  sunset  is  due  to  total  reflection  of  some  of  the  light  by 
the  atmosphere. 


CHAPTER   II. 


LENSES. 


WE  have  proved  (Figure  30)  that  when  the  surfaces  of  any  trans- 
parent medium  that  receive  and  transmit  light  are  not  parallel 
to  each  other,  that  refraction  occurs  to  the  transmitted  rays; 
that  the  degree  of  deviation  is  dependent  upon  the  relative  positions 
of  the  bounding  surfaces  (Figure  30),  the  angle  of  incidence  (Figure 
32),  and  the  index  of  refraction  (Figure  26).  The  medium  best 
adapted  to  general  use  for  purposes  of  optical  refraction  is  ^'Arw,  and 
in  speaking  of  the  refractive  medium  hereafter,  glass  will  be  meant 
unless  otherwise  indicated.  The  inde.x  of  refraction  of  glass  being 
known,  to  obtain  a  given  degree  of  refraction,  it  is  only  necessary  to 
determine  the  relative  positions  of  the  bounding  surfaces. 


ure  34. 
Optical  prUms;  A,  llie  apex;   B  C,  Iheba-e;   R,  incident  ray  refracted  to  D.        A'  B'  C    pos- 
fracting  powt 

Let  figure  34  represent  two  refracting  instruments,  ABC  and 
A'  B'  C ;  the  length  of  the  sides  A  B  and  A'  B'  are  the  same,  and  A  C 
and  A'  C  are  also  the  same  length.  B  C  is  shorter  than  B'  C ;  there- 
fore, the  angle  B  A  C  is  smaller  than  the  angle  B'  A'  C  It  has  been 
demonstrated  that  of  these  two  instruments  A'  B'  C  possesses 
the    greater    power   of  deviation    of   light,    so    that    if    the  lines  B  C 


LENSES. 


...    vieet 


and  B'  C  be  prolonged  as  straight  lines,  the  refracted  ray  R  will  i''.\s 
A  B  at  D  and  R'  will  meet  A'  B'  at  D';  the  distance  C  D'  will  be  /o''^ 
than  the  distance  C  D.  Such  a  refracting  instrument  is  called  a 
/n's;//. 

Ail  optical  prism  is  a  piece  of  glass,  or  other  transparent  material, 
zcl/ose  t-Li'o  plane  surfaces  that  receive  and  transmit  light,  form  a)! 
angle  with  each  other.  The  line  where  the  surfaces  meet  is  called  the 
apex  of  the  prism,  the  third  surface  of  the  prism  is  called  its  base.  In 
figure  34  the  apex  of  the  prism  A  B  C  is  at  A,  the  base  is  B  C. 

A  prtsm  alieays  refracts  light  toieanl  its  l>asc. 


Figure  35. 

■Optical  effects  of  a  prism;   R  D.  incidenl  ray,    D  E   refracted  ray  hent  toward  tlie  base    BC; 

R,  actual  position  .^f  object;  R.  apparent  position    of   object    toward    tlie    apex 

when  viewed    from  E  tlirough  the  prism. 

The  position  of  an  object  is  apparently  in  the  direction  from 
which  the  rays  of  light  from  the  object  enter  the  eye.  Figure  35  re- 
presents a  prism  A  B  C,  the  ray  R  is  refracted  at  the  point  D  toward 
the  base  and  enters  the  eye  placed  at  E  as  coming  in  the  direction 
D  E;  if  E  D  is  extended  back  through  the  prism  in  a  straight  line, 
it  will  pass  through  the  point  R'  and  to  the  eye  the  ray  will  appear 
as  coming  from  R',  which  will  seem  to  be  the  location  of  the  object 
situated  at  R 

The  optical  effect  of  a  prism  is  to  refract  light  toivard  its  base,  but 
an  object  seen  through  a  prism  appears  displaced  toward  its  apex. 

If  two  prisms  of  equal  measurements  be  placed  base  to  base,  two 
rays  incident  upon  identical  points  of  each  prisin  will  meet  after  re- 
fraction at  the  same  point  upon  a  line  that  is  an  extension  of  their 
base  line,  if  the  incident  rays  are  parallel  to  this  line 

Figure  36  will  represent  three  forms  of  prism  ABC,  each  placed 
base  to  base  with  a  corresponding  prism  D  B  C.  The  rays  R  and  S 
are  parallel  to  the  line  B  C  and  the  incident  points  E  and  F  are  identi- 
cal points  upon  the  surfaces  A  B  and  D  B.  By  identical  points  it  is 
meant  that  one  point  is  located   upon  one  surface  in  a  position  corre- 


OCULAR 


R  K  F   R  A  C  T   I  O  N. 


spending  to  the  location  of  the  other  point  upon  the  second  surface. 
The  ray  R  is  refracted  and  if  B  C  is  extended  as  a  straight  line,  R 
will  meet  B  C  at  a  point  indicated  as  P;  the  ray  S  will  also  be  refract- 
ed in  a  similar  manner  and  its  path  intersects  B  C  at  P  also. 

As  a  circle  may  be  regarded  as  a  regular  polygon,  that  is,  a  plane 
surface  bounded  by  straight  lines  of  equal  length,  and  of  infinite 
number;  so  a  sphere  may  be  regarded  as  a  body  bounded  by  an  infi- 
nite number  of  equal  plane  surfaces. 

If  a  section  be  cut  from  a  sphere  so  that  the  surface  made  by  the 
cut  be  a  plane,  we  have  a  body  bounded  by  one  plane  and  one- curved 
surface,  every  point  upon  the  curved  surface  will  be  equally  distant 
from  the  centre,  (Figure  13),  the  curvature  must  therefore  be  the  same 
in  all  meridians.      If  the  spherical  body  be  of  glass,  we  have  a  refract- 


1  effects  upon 


Figure  36. 

allel   to   base   line    B  C    of  corresjx 
It  upon  identical  points  E  and  F. 


ing  medium  whose  power  is  alike  in   all   meridians,  as  the  relation  of 
the  two  surfaces  to  each  other  is  the  same  in  all  meridians. 

The  surface  made  by  the  cut  may  be  concave  or  convex  as  well  as 
a  plane,  the  three  conditions  are  shown  in  figure  37.  Consider  that 
the  surface  A  C  D  is  made  up  of  an  infinite  number  of  small  planes 
I.  2,  3,  4,  5,  6,  7,  etc;  the  refractive  condition  created  is  that  of  two 
pri'^Tis  of  like  measurements  with  their  bases  together.  According  to 
the  law  of  refraction  and  the  experiment  illustrated  by  figure  36,  rays 
incident  upon  the  surface  A  P  D  meet  at  a  point  P  upon  a  line  pas- 
sing through  the  points  B  C  if  the  incident  rays  are  parallel  to  this 
line;  the  point  P,  where  the  parallel  rays  meet  after  refraction  by  a 
curved  surfaces  is  called  the  principal  focus. 


LENSES.  39 

A  transparent  incdiicn  having  one  curved  and  one  plaiic  surface,  or 
both  surfaces  curved,  and  having  the  poiver  to  bring  rays  of  light  to  a 
focus  is  cii/Zcd  a  /ens.  A  prism  is  not  a  lens,  though  it  lias  been  called 
such,  it  is  incorrect. 

The  forms  of  lens  shown  in  figure  37  are  designated  as  convex 
spliericals  as  they  are  sections  of  a  sphere ;  number  I  is  a  plano-convex, 
number  II  a  concavo-convex,  number  III  a  double  convex.  The  phy- 
sical characteristics  of  all  are  the  same,  they  are  thick  in  the  centre, 
thinner  at  the  periphery  (edge),  and  converge  rays  of  light  that  they 
transmit.  In  every  spherical  lens  there  are  two  points,  B  and  C  figure 
37,  one  upon  each  surface,  so  situated  that  a  straight  line  may  be 
drawn  through  these  two  points  and  the  centre  of  curvature  of  the 
surfaces;  a  ray  of  light  whose  path  follows  this  line  suffers  no  refrac- 
tion, this  line  is  called  the  principal  axis  oi  the  \er\s\  the  principal  focus 
of  a  lens  is  a  point  situated  upon  this  line  and  is  where  the  rays  that 
are  parallel  to  the  principal  axis  meet  after  refraction.    At  some  point 


Figure  37. 


Spherical  '. 


sph, 


upon  the  principal  axis  is  located  a  point  called  the  optical  centre  of 
the  lens,  in  number  III,  figure  37  it  is  located  half  way  between  the 
points  B  and  C.  The  optical  centre  of  a  lens  is  the  point  through 
which  rays  of  light  pass  without  being  refracted ;  this  due  tc  the  fact 
that  the  small  planes  upon  the  surfaces  of  the  lens  pierced  by  such  rays 
are  parallel  planes.  Any  ray  passing  through  the  optical  centre  of  a  lens 
except  that  traversing  tne  principal  axis,  forms  a  secondary  axis  which 
is  practically  an  unbroken  line,  the  incident  and  emergent  rays  being 
parallel  and  but  slightly  displaced  even  in  the  higher  power  lenses. 
ThQ  focal  /^wf//;  of  a  lens  is  the    distance    between  the  optical  centre 


O  C   U    L  A 


E  F 


ACT 


and  its  principal  focus;  the  greater  the  power  the  shorter  will  be  the 
focal  length. 

Concisely  described:  an  optical  lens  is  an  instrunient  niaiie  of  a 
transparent  niediuvi  that  refracts  light  according  to  an  established  sys- 
tem, it  is  nsually  of  glass,  of  a  hiunon  index  of  refraction,  loithtioo  sur- 
faces of  a  certain  ratio  of  cnrvatnre  giving  a  definite  focal  pozver. 

There  are  certain  forms  of  glass  used  in  spectacles  and  c  yeglasses 
that  are  commonly  called  lenses  but  that  are  not  correctly  designated 
any  more  so  than  that  a  prism  is  a  lens.  If  the  surfaces  of  a  piece  of 
glass  or  other  transparent  medium  be  parallel  as  shown  in  figure  29, 
there  is  no  refraction  and  we  call  such  a  piano  glass.       The  surfaces 


Convex  sphcri 


conclary 


may  also  be  curved  but  so  related  that  their  effect  is  the  same  as  if 
they  were  parallel  planes  and  there  is  no  refractive  power,  such  should 
be  called  curved  piano  glasses  and  not  lenses.  The  trade  (optical) 
name  for  such  is  coquille  and  mi  coquille  glasses. 

Figure  38  represents  a  double  convex  lens  A  B  C  D,  the  principal 
axis  will  be  G  P,  the  optical  centre  is  located  at  O,  the  rays  parallel 
to  the  principal  axis  are   converged  to  the  principal  focus  P.      If  light 


be  situated  at  the  principal  focus  of  a  convex  spherical  lens,  the  tays 
will  undergo  refraction  and  emerge  as  parallel.  If  the  light  be  placed 
between  the  principal  focus  and  the  lens  the  rays  will  emerge  diver- 
gent, but  not  so  divergent   as  they  enter;    if  the  light  be  beyond  the 


LENSES  41 

principal  focus  the  rays  will  emerge  convergent.  The  straight  line 
K  L  represents  a  secondary  axis,  as  it  passes  through  the  optical  cen- 
tre O. 

Figure  39  shows  a  convex  lens  whose  principal  focus  is  at  F, 
light  from  the  point  P  beyond  the  principal  focus  is  converged  and 
focused  at  P';  these  two  points,  P  and  P',  bear  a  certain  defined  rela- 
tion to  each  other  and  are  called  conjugate  foci;  either  may  be  taken 
as  the  location  of  the  luminous  point,  at  the  other  the  rays  will  be 
focused  and  form  a  real  image  of  the  luminous  point. 

To  show  the  formation  of  an  image  of  the  object  by  a  convex 
spherical  lens,  let  A,  figure  ^o,  represent  the  lens,  its  optical  centre 
at  O,  its  principal  focus  at  F;  L  and  M  indicate  two  points  upon  the 
-object  situated  a  greater  distance  from  the  lens  than  its  focal  length. 
The  path  of  a  ray  from  the  point  L  parallel  to  the  principal    axis   will 


of  image 
greater  vi 


Figure  40. 
ical  lens.     F,    Ihe  focus;    L  M.    the   object 
lens  than  its  locall  ength;  L'  M',  the  image, 
inverted  and  magnified. 


1)6  incident  at  E  and  will  be  refracted  through  the  principal  focus  F, 
the  path  of  another  ray  from  L  through  the  optical  centre  O  will 
meet  E  F  at  L'  which  will  locate  the  image  of  the  point  L ;  in  the  same 
way  locate  the  image  of  the  point  M  at  M'.  It  can  thus  be  shown  that 
light  frorn  every  point  upon  the  object  is  directed  to  its  corresponding 
position  in  the  image. 

j^  convex  spherical  lens  creates  a  real  inverted  image  of  an  object  by  focus- 
ing upon  a  screen  the  divergent  rays  from  every  point  upon  the  object,  the  collec 
tion  of  foci  creating  the  image. 

Take  a  convex  lens  L,  figure  41,  of  say  ten  inches  focal  length 
and  place  a  lighted  candle  at  its  principal  focus  A,  the  light  will  be 
refracted  as  parallel  rays  on  emerging  from  the  lens  and  the  image  of 


OCULAR 


REFRACTION. 


the  candle  will  be  at  infinity  (practically  no  image  is  formedj,  if  the 
candle  be  placed  at  the  point  C  twenty  inches  from  the  lens,  just 
double  its  focal  length,  a  sharp  image  of  the  t^ame  will  be  projected 
upon  a  screen  held  at  C'  twenty  inches  from  the  lens   and  this  image 


rure  41. 

Position  and  size  of  image  tornied  by  a  convex  spherical  lens,  the  object  in    various   positions 

with  regard  to  the  focus  of  the  lens      A  different  character  of  line 

joins  each  object  and  its  image. 

will  be  the  exact  size  of  the  flame.  If  the  candle  be  removed  further 
from  the  lens  than  twice  the  focal  length  say  to  D  thirty  inches  away, 
the  image  may  be  received  upon  a  screen  at  D'  fifteen  inches  from  the 
lens  and  the  image  will  be  smaller  than  the  flame,  in  fact  just  half  the 
size.  If  the  candle  be  placed  between  the  positions  A  and  C  at  B. 
that  is,  between  the  focus  and  twice  the  focal  length,  the  image  will 
be  larger  than  the  flame,  and  more  than  twice  the  focal  length  re- 
moved from  the  lens       If  the  candle  be  placed  at  E,  nearer  to  the  lens 


ing  tha 


than  its  focus  the  rays  will  emerge  divergent  as  shown  by  E'  E  and 
no  real  image  will  be  formed.  To  facilitate  locating  the  paths  of  rays 
from  the  various  positions  shown,  each  is  indicated  in  the  figure  by  a 
line  of  different  character. 


L   E  N  S  K  S  43 

The  size  of  the  image  created  by  a  convex  lens,  is  to  the  size  of  the  object,  as 
their  distances  from  the  optical  centre  of  the  lens  are  to  each  other. 

A  comparison  of  the  phenomena  illustrated  by  figures  41  and  22 
will  be  interestin.t,  and  instructive,  the  student  should  not  fail  to  make 
the  experiments  illustrated  by  figures  41  and  43. 

As  shown  by  figure  41,  rays  from  an  object  situated  nearer  to  the 
lens  than  its  focal  length  are  divergent  after  refraction,  the  image  thus 
created  is  virtual  only.  Let  figure  42  represent  a  convex  lens  A 
whose  focus  is  at  F,  the  object  being  placed  at  L  M  which  is  nearer  to 
the  lens  than  its  focal  length.  Let  a  ray  from  L  parallel  to  the  princi- 
pal axis  meet  the  lens  at  E  and  it  is  refracted  through  F',  another  ray 
from  L  through  the  optical  centre  forms  a  secondary  axis  L  O;  by 
extending  O  L  and  F'  E'  upon  the  same  side  of  the  lens  as  the  object 
we  find  their  virtual  focus  and  thus  locate  the  virtual  image  of  L  at 
L'.  In  the  same  way  locate  the  virtual  image  of  the  point  M  at  M'; 
it  is  found  that  the  image  is  erect,  virtual  and  iitagnificd.  This  property 
of  a  convex  lens  is  made  use  of  to  construct  an  instrument  called  a 
microscope;  the  action  of  a  simple  microscope  can  be  nicely  demon- 
strated by  the  following  experiment. 


I 


Figure  43. 

Object  I.  viewed  through  a  convex  lens;    II.    the  lens  held  nearer  the  object   than    its   foca 
length;  III.  the  lens  held  beyond  its  local  length. 

Draw  a  figure  similar  to  I,  figure  43  upon  a  sheet  of  paper,  before 
it  hold  a  strong  convex  lens  quite  close  to  the  paper,  the  eft'ect  shown 
by  II  will  be  created,  the  figure    will   appear  erect  and  magnified;  if 


44  OCULAR         R  E   F  R  A   C  T  I  O  N. 

the  lens  be  withdrawn  gradually  from  the  figure  it  increases  in  size 
rapidly,  remaining  erect  and  finally  disappears,  wnich  indicates  the 
focus  has  been  reached.  Removing  the  lens  still  further  the  figure 
reappears  as  shown  by  III,  it  is  inverted  and  magnified  and  as  the  lens 
is  still  further  withdrawn  its  size  is  diminished. 

All  the  rays  from  any  point  of  an  object  do  not  meet  after  refrac- 
tion by  a  spherical  lens  at  exactly  the  same  point  and  this  creates 
what  is  known  as  spherical  aberration.  The  result  of  spherical  aber- 
ration is  to  give  a  blurred  image  and  create  distortion. 


Figure  44. 

Spherical  abenatioii;    F,  approximate  focus  ot  central  rays;    G  that  of  the  marginal  rays. 

Figure  44  illustrates  the  principles  of  aberration  of  a  spherical 
lens  L;  the  rays  incident  upon  the  lens  form  varying  angles  with  the 
small  planes  of  the  surface,  the  ray  whose  path  follows  the  principal 
axis  is  normal  to  the  plane  at  the  point  of  incidence  while  the  path  of 
a  ray  that  is  incident  upon  a  plane  at  the  periphery  forms  the  greatest 
angle  of  incidence.  The  rays  that  are  refracted  by  the  central  por- 
tion of  the  lens  have  their  focus  approximately  at  F  while  those  that 
are  refracted  by  the  edge  of  the  lens  have  a  focus  approximately  at 
G,  a  point  nearer  to  the  lens.  This  would  prove  that  the  edges  of  a 
spherical  lens  possess  greater  power  of  refraction  than  the  centre, 
and  this  is  true,  the  effects  created  are  not  so  noticeable  in  the  weak- 
er power  lenses  as  m  the  stronger  ones,  a  lens  of  two  inches  so  called 
focus  has  a  focal  power  at  the  periphery  of  about  1.6  inches,  which 
gives  a  quite  blurred  image.  The  degree  of  aberration  increases  with 
the  size  (aperture)  of  the  lens  and  the  power,  also  the  form  of  the 
lens  and  the  distance  of  the  object  A  double  convex  lens  has  the 
greatest  aberration,  and  gives  the  most  distortion,  a  piano  convex 
less,  and  a  periscopic  the  least. 

Persons  who  have  worn  glasses  for  years  of  a  certain  form  find  it 
difficult  in  some  instances  to  use  the  same  power  lens  but  in  another 
form;  it  will  be  well  to  remember  this  fact  as  it  may  explain  what 
may  otherwise  seem  to  be  an  imaginary  grievance  of  some  glass 
wearer.      In  cameras  and  some  other  optical  instruments,  the  aberra- 


LENSES.  45 

tion  is  corrected  by  the  use  of  a  diaphragm  that  cuts  out  the  periph- 
eral rays  and  sharpens  the  image.  In  the  eye  this  diaphragm  effect 
is  supplied  by  the  iris. 


Figure  45. 

Distortion  of  objects  created  by  looliing  through  strong   convex   lenses,    the  square   S  is  dis- 
torted into  the  curved  sided  figure  S';  etc. 

Figure  4J  shows  how  objects  appear  distorted  when  viewed 
through  a  strong  convex  spherical  lens,  the  two  vertical  parallel  lines 
A  and  B  are  greatly  magnified  when  seen  through  the  lens,  they  are 


V 


I  rgure  46. 

A    plano-convex;  B,  concavo-con 
id  D,  bi-convex  or  double  convex 


Types  of  convex  spherical  lens. 

copic;  C  i 

no  longer  straight  but  appear  as  two  curved  lines  A'  B'  with  their  con- 
vex sides  toward  each   other.       The  square  figure  S  becomes  a  figure 


46  OCULAR         REFRACTION. 

S'  bounded  by  four  curved  sides,  their  convexity  toward  the  centre. 
A  familiar  evidence  of  spherical  aberration  is  seen  in  photographs  of 
street  scenes  in  which  the  buildings  have  the  appearance  of  being 
about  to  topple  into  the  centre  of  the  street,  the  effect  is  created  by 
the  spherical  aberration  of  the  lens  of  the  camera. 

The  sections  cut  from  the  transparent  spherical  body  illustrated 
by  figure  37,  to  which  has  been  given  the  name  of  convex  spherical 
lenses,  types  of  which  are  shown  in  figure  46;  A  being  a  piano  con- 
vex, B  a  concavo  convex  or  meniscus  (also  called  a  periscopic),  C  and 
D  double  or  bi-convex.  These  lenses  all  have  certain  optical  proper- 
ties that  are  alike.  If  we  place  them  upon  a  sheet  of  paper  and  with 
a  pencil  outline  the  edge,  the  figure  drawn  will  be  a  circle,  see  I,  fig- 
ure 47;  draw  two  lines  at  right  angles  to  each  other  that  will  be  dia- 
meters of  the  circle  and  they  will  intersect  at  the  centre,  place  the 
lens  upon  this  figure  so  that  its  edge  corresponds  to  the  circumference 


Figure  47. 
Marking  tliegeomelric  and  optical  centres  ol  a  Itns. 

of  the  circle  and  with  india  ink  and  a  fine  hard  wood  point  (a  piece  of 
"  jewelers  peg  wood  "  makes  the  best  point  for  this  purpose)  mark 
carefully  at  the  periprery  of  the  lens  the  four  points  A  A'  B  B',  indi. 
eating  where  the  diameters  meet  the  circumference;  also  mark  a 
cross  at  O  to  indicate  the  centre,  the  lens  will  thus  appear  as  shown 
by  II,  figure  47.  The  cross  will  thus  mark  the  gfoiiicti-ical  centre  of 
the  lens  and  also  its  optical  centre,  being  the  point  upon  its  surface  in 
the  principal  axis. 

By  figure  37  it  is  demonstrated  that  the  ray  traversing  the  princi- 
pal axis  and  therefore  passing  through  the  optical  centre  is  not  re- 
fracted.    If  we  draw  a  vertical  straight  line,  I,  figure  48,  upon  apiece 


of  paper  and  hold  the  lens  so  that  in  looking  at  the  line  S  L  through 
it  our  line  of  vision  follows  the  principal  axis,  the  line  will  appear 
unbroken  and  passing  through  the  points  A  and  A'  as  shown  by  II, 
figure  48.       Move   the  lens  to   the   rig/it  in  the   same  plane,  and  the 


"he  appearance  of 


appearance  created  will  be  illustrated  by  III,  figure  48,  the  points  A 
and  A'  will  appear  to  the  right  of  the  line  S  L  while  the  portion  of 
the  line,  S'  L',  seen  through  the  lens  will  appear  displaced  to  the  Icf/. 


Cause  of  apparent  displacment  of  objf 


Figure   49. 

ct  by  convex  spherical  lens;  also  comparison 


f  degree 


This    phenomena  will    be  explained   by   reference  to  figure  49,  I 
represents  the  first  position  o:  the  lens,  the  visual  line  from  the  eye  at 


E  to  the  object  A  corresponding  to  the  principal  axis;  II  represents 
the  second  position  of  the  lens,  the  visual  line  now  passed  through  a 
prism  and  the  object  while  actually  occupying  the  same  position  as 
before  at  A  appears  displaced  to  A'  toward  the  apex  of  the  prism,  (fig- 
ure 35)  this  gives  foundation  for  the  following  law. 

I'V/u-ii  ail  object  is  :w'i-:^',-(/  tliroiii:;li  a  convex  spherical  /ens  and  the 
lens  is  nioi'cd  laterally,  the  object  appears  to  move  in  the  opposite  direc- 
tion. 

The  amount  of  displacement  that  the  object  appears  to  undergo, 
depends  upon  the  power  of  the  prism  (strength  of  the  lens)  and  the 
distance  from  the  lens  ot  the  object  viewed.  If  the  object  were  situ- 
ated at  A,  shown  by  II,  figure  49,  it  would  appear  as  displaced  to  A' 
while  if  at  B,  a  position  nearer  the  lens,  it  would  seem  to  be  located  at 


Appearance  of  \ 


;ure  50. 

al  line  seen  tlirovigh  convex  spherical  lens  rotat 
lot  displaced,  no  displacement  of  the  line  S  L. 


:d    about    its   centre    but 


B';  the  distance  from  A  to  A'  is  greater  than  that  from  B  to  B',  though 
each  is  created  by  the  same  movement  of  the  lens  L. 

The  stronger  the  lens  and  the  greater  the  distance  of  the  object  from 
it,  the  more  rapid  zvill  be  the  movement  of  the  object. 

If  an  object  be  viewed  through  a  spherical  lens,  the  lens  may  be 
rotated  upon  its  principal  axis  and  the  object  will  not  be  distorted  by 
the  act  of  rotation. 

Figure  50  will  illustrate  the  straight  line  S  L  seen  through  the 
lens  in  various  positions  rotated  about  its  centre,  so  long  as  the  lens  is 
not  displaced  but  merely  rotated,  no  change  in  the  appearance  of  the 


L  E  N 


49 


object  is  created,  for  the  spherical  lens  possesses  like  power  in  every 
meridian. 

A  coiivc.v  spltcrical  lens  zl'UI  />,■  rcci\i;i!i.::cd;  first,  br  the  fact  that 
upon  rotating  it  no  distortion  occurs  of  an  object  viciccd  through  it; 
second,  look  througli  it  at  sonic  o/>jcct  at  as  great  a  distance  as  possible, 
preferably  a  vcrtual  straight  line,  and  viove  the  lens  back  and  forth 
zoith  a  pendulum  like  motion,  if  convex  the  object  zoill  move  opposite  to 
the  movement  of  the  tens. 

"  Uncut  lenses  "  are  sold  by  the  makers,  having  a  given  focus 
but  not  edged,  the  blanks  average  about  45  millimeters  square;  from 
these,  lenses  of  various  forms  may  be  cut.  In  order  to  find  the  optical 
centre  of  these  irregular  shape  lenses,  draw  upon  a  paper  two  straight 
lines  in  the  form  of  a  cross,  the  lines  must  be  at  right  angles  to  each 


Figur 


1!;  the  opli 
^  angles  k 


51- 

irregular  shape  spherical  lens;  PI.  tlie  straigh 
unbroken,  indicating  centre  where  ihey  intei 
ppearance  in  another  position. 


ri.ht 


other,  hold  the  lens  in  such  a  position  before  the  crossed  lines  that 
they  appear  unbroken  through  the  lens  as  shown  by  II,  figure  51,  any 
deviation  from  this  position  will  create  an  effect  smiilar  to  that  illus- 
strated  by  I,  figure  51.  Having  located  the  centre,  mark  the  irregu- 
lar lens  the  same  as  was  done  in  figure  47,  and  the  form  for  the  de- 
sired size  and  shape  lens  can  now  be  imposed  with  its  geometric  cen- 
tre upon  the  optical  centre  of  the  lens  and  this  form  outlined  upon  the 
blank,  this  will  give  a  properly  cent  red  X&m.     To  ascertain  if  any  lens 


R  E  F  R  A   C  T  I  O  X. 


is  properly  centred,  proceed  as  above  and  see  if  the  optical  and  geo- 
metrical centres  correspond.  Sometimes  it  is  desired  to  dccoitrc  a 
lens,  or  to  have  the  optical   centre   located  in  a  certain  position   with 


tres  of  lens  identical;  II.  geometric  cenlre  purposely  displaced 


regard  to  the  geometric  centre.       I,  iigure  52,  shows  a  centred  lens, 
II,  figure  52,  a  decentered  one  marked  out  upon  the  blank. 


4 


Figure  53. 
Optical  effects  cf  corresponding  prisms  apices  togetlier^u 


parallel  rays  of  light. 


In  figure  36,  pairs  of  similar  prisms  base  to  base  are  shown, 
figure  53  shows  the  optical  effect  of  pairs  of  similar  prisms  with  their 
apices   together.       C  is  the  apex  of  the  prisms  A  C  B  and  D  C  E,  the 


LENSES. 


ray  K  L  is  not  refracted,  but  the  rays  R  and  S  incident  upon  the 
identical  points  G  and  H  are  refracted  alike,  and  from  being  parallel 
are  rendered  divergent.  Figure  ^  illustrates  a  form  of  optical 
instrument    having    surfaces    that  are  sections  of  a  sphere  so  related 


: spher 


R,  incident 


Figure  54. 

s;    R',  refracted 


cus;  r.  O,   principal 


that  they  have  certain  optical  properties.  Figure  54  represents 
another  form  of  lens  having  two  spherical  surfaces  so  related  that 
they  create  optical  effects    that    are  exactly   the  opposite  of  convex 


Types  of  ( 


:  spherical  lens;  A,  piano  concave 
scopic;  C  and  D,  bi-concave 


iicave,    meniscus 


spherical  lenses,  they  are  termed  concaii  ^pluinal  lenses.  It 
will  be  seen  that  the  parallel  rays  R  in  palssing  through  the  concave 
lens  L  are  refracted  as  divergent  rays  R'  and  therefore  can  never 
meet,  so  that  they  are  not  brought  to  a  focus.  A  concave  lens  there- 
fore has  no  real  fccus  but  only  a  inrtiial  focus  which  is  located  by  ex- 


tending  the  divergent  rays  back  to  a  point  where  they  would  meet, 
as  P  figure  54.  Various  types  of  concave  spherical  lenses  are  illus- 
trated by  figure  55 ;  A  is  a  plano-concave,  B  a  convexo  concave,  or 
periscopic,  C  and  D  double  or  hi  concave.  It  will  not  be  necessary 
to  go  all  over  the  characteristics  of  the  concave  lens  as  they  are  simi- 
lar to  those  of  the  convex,  but  of  the  opposite  effect.  A  few  words 
however  will  not  be  amiss.  They  are  thin  in  the  centre,  thicker  at  the 
periphery,  possess  the  same  faults  of  aberration  and  distortion,  if  they 
are  rotated  upon   their  centre   they  do  not  distort    the   object  viewed 


Appea 


Figure  56. 

:  of  an  object  I'hrougl]  a 


Dncave.ph. 


through  them.  They  are  centred  or  decentred  in  the  same  way.  The 
effect  created  by  looking  through  such  lenses  is  to  make  the  object 
appear  smaller;  figure  56  shows  a  figure  I  of  a  certain  size  and  form, 
II  shows  this  same  figure  seen  through  a  concave  lens  at  a  given  dis- 
tance, III  the  same  figure  with  the  lens  fuither  removed,showing that 
the  greater  the  distance  of  the  object  from  the  lens  the  smaller  it  will 
appear  to  be. 

Repeat  experiment  illustrated  by  figure  50,  using  a  concave  lens 
and  no  difference  will  be  detected  between  the  convex  and  concave; 
however,  if  experiment  illustrated  by  figure  48  be  made  with  a  con- 
cave lens  the  results  will  be  shown  by  figure  57.  The  lens  being 
moved  to  the  right,  the  portion  of  the  line  vS'  L'  seen  through  tne  lens 


L  E  N  S  E  S. 


53 


also  appears  to  the  right  of  the  line  S  L  or  with  the  movement  of  the 
lens. 

A  convex  lens  can  be  distins^nished  from  a  concave,  by  the  fact  that 
an  object  moves  against  the  lens  movement  of  a  convex,  and  loith  the  lens 
if  it  be  concave. 

In  the  chapter  on  light  it  was  explained  that  light  was  composed 
of  rays  of  various  wave  length  that  gave  the  effect  of  color,  a  prism 
possesses  the  power  of  separating  white  light  into  its  component  parts. 
If  a  band  of  light  be  admitted  through  a  slit  A  figure  58,  and  trans- 
mitted by  a  prism  P  upon  a  screen  S,  it  will  be  separated  into  a 
luminous  band  showing  the  colors  of  the  spectrum,  this  is  termed  the 


ppearanceof  a  vertical  straight  line  tlirougli  acoiua 

e  spherica 

vision  passing  through  the  optical  centre;  III.  lens 

moved  to  t 

displaced  to  the  right. 

•ighl 


dispersion  of  light  and  is  due  to  the  difference  of  ihe  degree  of 
deviation  of  the  various  rays  by  refraction  Red  is  deviated  the  least 
and  is  said  to  be  the  least  refrangible  color,  and  in  the  order  of  re- 
frangibility  come,  orange,  yellow,  green,  blue  and  violet,  the  violet 
being  the  most  refrangible  color.  This  creates  in  lenses  what  is 
termed  chromatic  aberration,  the  images  fonned  by  strong  spherical 
lenses  are  tinged  with  these  colors. 

In  figure  58  the  spectrum  color  band  is  shown  as  having  seven 
colors,  but  it  is  merely  a  sub  division  of  the  blue  into  two  shades, 
cyan  blue  an  :  ultramarine  blue,  according  to  a  later  idea  of  the 
spectrum. 


54  OCULAR         R   L  F  R   A  C  T  I  O  N. 

Having  found  that  various  powers  may  be  obtained  in  lenses, 
some  method  of  numbering  or  indicating  their  power  must  necessarily 
be  devised.  Almost  all  knowledge  is  obtained  by  comparisons  with 
something  that  we  can  easily  comprehend,  thus  we  form  our  estimates 
of  height,  distance,  value,  etc.  by  adopting  some  definite  //////  with 
which  to  calculate  multiples  or  sub  divisions.  As  the  most  convenient 
property  of  a  lens  upon  which  to  base  a  system  of  numbering  is  to 
measure  its  length  of  focus  it  was  natural  to  note  this  in  inches,  the 
inch  being  the  linear  unit.  A  /ens  Iiaving  a  focal  length  of  one  inch 
was   therefore  adopted  as  the   unit,  this  really  established  a  uniform 


Disper: 


by  a  pri: 


ed  bv 


Figure   58. 

Band  of  light  passing  through  slit  .A,    t 
P,  forming  spectrum  band  S. 

system  of  numbering  which  was  a  great  improvement  over  older 
methods,  by  which  each  lens  grinder  distinguished  certain  lenses  by 
a  name,  or  a  number  that  represented  a  totally  different  value  from 
that  of  another  maker.  While  an  improvement,  the  "  inch  system  '' 
left  much  to  be  desired.  Of  a  one  inch  lens  it  may  safely  be  said, it  is 
never  used  in  the  correction  of  an  error  of  refraction,  those  that  are 
used  being  weaker,  it  is  necessary  to  indicate  their  value  in  fractions. 
A  lens  having  a  length  of  focus  of  four  inches  would  be  of  but  one- 
fourth  the  power  of  the  unit,  one  of  thirty-si.x  inches  focus  should  be 
termed  a  onethirty-sixth.  From  this  method  it  has  become  custom- 
ary to  speak  of  a  number  ten  lens,  meaning  really  a  one-tenth  focal 
power;  a  number  twenty-four  is  a  one  twenty-fourth;  the  larger  num- 
ber thus  indicated  the  weaker  power. 


So  long  as  the  use  of  glasses  was  confined  to  aiding  elderly  peo- 
ple to  read  and  work  at  close  point  with  more  comfort,  and  now  and 
then  helping  a  near  sighted  person  to  enjoy  better  vision,  the  glasses 
being  merely  convex  or  concave  sphericals,  and  the  calculations  being 
of  the  simplest  kind  compared  to  those  of  to-day,  this  system  answered 
fairly  well.  With  the  increase  of  the  knowledge  of  optics  and  the 
consequent  widening  of  the  optical  field,  due  to  a  growing  demand  for 
glasses,  it  having  been  discovered  that  they  could  bring  relief  to 
young  and  old  alike,  the  inch  system  proved  too  awkward  to  handle. 
The  greatest  objection  is  the  fact  that  in  combining  lenses  of  different 
character  and  focus  the  calculations  had  to  be  made  in  fractions. 
Suppose  that  it  is  desired  to  combine  a  one-fifth  and  a  one  twenty- 
si.xth  lens,  it  is  necessary  to  resort  to  pencil  and  paper  with  this 
result: — 

I  I  26  q  -ji  I 


5         26        130       130        130        4    6/31 
This  is  an  every  day  experience  and  with  a  busy  operator  would  have 


Eq>. 


spill 


Figure  59. 

tained  by  unequal  cuivatures,    the  pc 
,t  of  the  two  surfaces  combined. 


of  the  lens  being 


to  be  done  many  times  a  day;  the  liability  to  error,  and  its  inaccu- 
racy is  plainly  seen;  leaving  out  entirely  any  consideration  of  the 
time  required  for  such  calculations. 

The  decimal  system  was  advocated  and  the  logical  result  was  a 
resort  to  the  "  metric  system."  Profiting  by  the  experience  with  the 
inch  system,  a  weaker  power  was  selected,  and  a  lens  having  a  focal 
length  of  one  meter  was   adopted    as    the    unit.     To  this  system  was 


56  O  C   U   L  A  R         R   K   F    R  A  C   T   I   O  X. 

given  the  name  ''Dioptric;"  the  standard  lens  was  said  to  be  cr  ^//r 
diopirv  Av/j.- and  had  a  focus  of  one  meter;  a  four  dioptry  lens  has 
four  times  the  power  of  the  unit  and  therefore  focuses  at  one  fourth 
of  a  meter.  By  comparison,  the  meter  is  found  to  be  39.5  inches  in 
length,  but  for  convenience  of  transposing  inches  into  dioptries,  or 
dioptries  into  inches,  it  is  considered  to  be  40  inches.  A  simple  rule 
for  the  transposition  of  a  lens  from  the  numbering  of  one  system 
into  that  of  the  other  is  as  follows: 

Divide  ^o  bv  the  number  of  the  lens  expressed  in  inches,  the  result 
icill  be  its  value  in  dioptries.       Divide  70  /']-  the  number  expressed  in 
dioptries,  the  result  i^' ill  be  its  focus  in  inches. 
Examples: —         40—10  inches  =  4.00  dioptries. 

40  --  13     "  =  3°o 

4  o  -•-  1 6      "  =2.50  " 

40  -^  26      "  =  r.50  " 

40  -r  S-oo  dioptries  =        8  inches 

40  —  0.50         "  =        80     " 

40  -;-  1.25         "         =        32     " 

40  -|-  8. 00  ■'  =  S      " 

For  comparison,  suppose  we  take  the  same  example  we  had  in  inches 
to  combine;  a  one  fifth  lens  is  eight  dioptries,  a  one-twenty-sixth  is 
one  and  a  half  dioptries. 

8.00  dioptries  +  i  50  dioptries  =  9.50  dioptries. 
This  calculation  can  easily  be  made  without  the  aid  of  paper  and  pen- 
cil and  in  a  moment,  its  advantages  over  the  other  system  are  obvious. 
Another  defect  in  the  inch  system  that  does  not  obtain  in  the 
dioptric  system,  is  the  lack  of  uniform  differences  between  the  lenses, 
thus:— the  difference  between  a  1/7  and  a  i/S  inch  lens  is  1/56,  while 
the  difference  between  the  next  successive  numbers  a  1/8  and  a  1/9 
inch  lens  is  1/72.  This  difference  between  successively  numbered 
lenses  is  greater  as  they  increase  in  power;  the  interval  between 
any  two  successive  lenses  is  never  the  same  as  that  between  any 
other  two  successive  lenses  numbered  by  the  inch  system.  In  the 
dioptric  system  of  numbering  ihe  differences  are  regular.  The 
dioptry  is  readily  sub  divided  to  indicate  the  power  of  le  ses  weaker 
than  the  unit,  one-half,  one  fourth  and  one-eighth  are  indicated 
respectively  as  0.50,  0.25  and  0.12.  This  may  seem  to  be  carrying 
the  system  to  extremes,  but  such  power  lenses  are  used  daily  in  the 
correction  of  the  errors  of  refraction  with  decidedly  beneficial  results 
so  that  they  occupy  an  important  place  in  the  field  of  optics  and  are 
constantly  involved  in  necessary  calculations 


The  Oi-^ti 


a.  Journal  &  Review 
LIBRA  BV 


LENSES. 


A  comparative  table  of  the   dioptric  and   inch    systems,  showing 
the  approximate  value  in  inches  is  here  given. 


Dioptric  System. 

Inch  System. 

O  12 

320 

0.25 

.60 

0-37 

108 

0.50 

80 

0.62 

60 

°-75 

52 

0.87 

44 

1. 00 

40 

1. 12 

36 

1-25 

32 

1.50 

26 

"•75 

22 

2. CO 

20 

2.25 

18 

2.50 

16 

2-75 

14 

3.00 

13 

3  25 

12 

350 

1 1 

3-7S 

10 

-■i 

400 

10 

450 

9 

5.00 

8 

5-50 

6.00 

1-2 

6.50 

7.00 

\    2 

8  00 

9.00 

1-2 

10.00 

11.00 

t-2 

12.00 

1-4 

13.00 

14.00 

3  4 

16.00 

1-2 

18  00 

1-4 

20.00 

40.00 

OCULAR 


REFRACT 


The  adoption  of  the  dioptric  system  is  one  of  the  signs  of  pro- 
gress of  optics  from  a  commercial  to  a  professional  basis,  and  its  ad- 
vance to  a  science. 

To  make  the  system  complete  and  more  convenient  for  the 
purpose  of  calculations  and  record,  certain  arbitrary  signs 
and  abbreviations  are  adopted.  Spherical  is  written  Sph. 
or  S;  dioptry  is  abbreviated  to  D.  ;  dioptric-spherical  is  short- 
ened to  D.  S.  or  D.  Sph.  The  sign  -f  (plus)  is  the  conventional 
mark'used  to  indicate  convex  curvature  of  a  lens  surface  while  the 
sign    for    concave    curvature    is   —    (minus).  These   same    signs 

are  also  used  to  indicate  the  character  of  a  lens;  thus,'  the 
sign  -f-  means  a  convex  lens,  the  sign  —  signifies  a  concave  lens.  A 
lens  may  have  a  —  (concave)  curvature  upon  one  surface  and  a  -|- 
(convex)  curvature  upon  the  other;  its  +  (convex)  or —  (concave) 
refractive  value  will  depend  upon  which  is  the  greater.  In  figure  59, 
C  represents  a  lens  having  a  —  1.25  D.  curvature  upon  one  surface,  a 
+  5.25  D    upon  the  other, the  value  of  the  lens  is  a  +  4.00  D.      These 


Equal 


W 


'B  —I  ecu 


Figure  60. 

spheric.il  value  witl 


are  the  usual  curvatures  for  "  Periscopic  "  lenses  of  convex  value,  a 
—  1.25  D. being  used  for  the  posterior  (inner)  surface  and  the  required 
convex  being  given  the  anterior  (outer)  surface.  The  concave  cur- 
vature is  placed  next  to  the  eye.  A,  figure  59,  shows  a  plane  surface 
ocmbined  with  a  -|-  4  00  D.  curvature;  B,  figure  59,  illustrates  a 
+  2.00  D.  curvature  on  each  surface  of  the  lens;  the  refractive  values 
of  A,B  and  C, figure  59  are  all  alike.  Figure  60  represents  lenses  hav- 
ing a  concave  value,  D  has  a  plane  surface  combined  wiih  a  —  4.00  D. 


E  S. 


59 


curvature,  E  a  —  2.00  D.  upon  each  surface,  Fa  —  i.oo  D.  upon  one 
surface,  with  a  —  3.00  D.  on  the  other,  G  the  usual  form  of  periscopic 
concave  lens,  +  1.25  D.  upon  the  anterior  surface,  —  5.25  D.  on  the 
posterior,  the  concave  surface  is  placed  toward  the  eye.  All  the  forms 
represented  by  figure  60  are  of  the  same  power. 

The  following  shows  various  forms  of  correctly  written  lens 
values  in  the  dioptric  system,  those  in  the  first  column  are  to  be  pre- 
ferred as  admitting  of  less  error,  beside  being  simple  and  to  the  point. 


+  1.00  D.  S. 

+  ■.ooD.  Sph. 

+  I.  Sph. 

+  ..  D. 

+  0  75  D.  S. 

+    -75  S. 

+  •75  D- 

+  .75  Sph. 

+  2,50  D.  S. 

+  2.5  Sph. 

+  2  1/2  S. 

+  2.50  Sph 

—  I  50  D.  S. 

—  1.50  D. 

-i.S  Sph. 

-KSS. 

-  0.50  D.  S. 

—  0.50  S. 

-.5D. 

—  .50  Sph. 

Figure  61. 
Formation  of  a  geomeliic  cylinder. 

Having  become  familiar  with  the  optical  properties  of  sections 
cut  from  a  transparent  sphere,  to  which  has  been  given  the  name  of 
spherical  lenses,  we  will  now  consider  another  form  of  lenses  that  are 
sections  of  a  different  form  of  solid  body  having  a  curved  surface, 
that  is,  a  cylinder.  Everyone  knows  in  a  general  way  what  the  form 
ot  a  cylinder  is,  it  might  readily  be  said  that  a  section  of  a  piece  of 
pipe  or  tubing  is  a  cylinder,  that  a  round  lead  pencil  is  a  cylinder; 
but  it  will  be  just  as  well  to  give  a  little  more  definite  description, 
and  to  that  end  we  will  consider  Us  important  characteristics. 


6o  O  C  f   L  A   K         K  E   K   K  A  C   T   I  O  X. 

Let  I,  figure  6i,  represent  a  rectangle  ABC  D,  its  opposite  sides 
are  equal  in  length  and  its  angles  are  all  right  angles.  Suppose  the 
side  A  B  to  be  fixed  and  the  rectangle  to  revolve  about  it  as  an  axis. 
The  body  illustrated  by  II,  figure  6i,  would  be  created.  The  bases 
would  be  circles,  A  being  the  centre  of  one,  B  the  centre  of  the  other 
and  the  axis  A  B  will  be  perpendicular  to  the  plane  of  both  bases.    If 


Figure  62. 


Formalion  of  a  cvlindric 


such  a  cylinder  were  made  of  glass  I,  figure  62,  and  a  section  were  cut 
from  it,  the  line  of  the  cut  being  parallel  to  the  axis  and  the  surface 
made  b}-  the  cut  being  a  plane,  an  optical  instrument  called  a.f>lane 
cylinder  11,  figure  62  would  be  created.  X  S  indicates  the  axis  of  the 
cylindrical  body  and  X'  S'  indicates  the  axis  of  the  cylinder  lens. 

If  the  cylindrical  body  I,  figure  62  were  to  be  cut  straight  through 
along  its  axis,  the  appearance  of  its  cross  section  would  be  as  illustra- 
ted by  I,  figure  6j,  that  is,  a  rectangle;  if  however  the  cut  were  to  be 
made  at  right  angles  to  the  axis,  a  very  diflierent  figure  would  illus- 
trate its  cross  section,  II,  figure  63  being  a  circle.  If  the  cylinder 
lens  II,  figure  62  were  cut  through  its  axis,  its  cross  section  would  be 
illustrated  by  III,  figure  63,  while  if  the  cut  were  made  at  right  angles 
to  its  axis, its  cross  section  would  present  the  appearance  of  IV,  figure 
63.  It  is  known  that  if  a  piano  convex  spherical  lens  be  cut  through 
its  optical  centre  along  any  meridian  the  cross  section  would  have 
exactly    the    same    appearance  as   shown    by    IV,  figure  63.      By  the 


LENSES.  6i 

appearance  of  III,  figure  ''3  it  is  seen  that  the  cylinder  possesses  no 
refractive  power  in  this  meridian,  the  surfaces  being  parallel  along 
these  lines,  the  optical  effect  of  the  cylinder  in  this  meridian  is  there- 
fore that  of  planoglass;  in  the  meridian  at  right  angles  to  this,  by 
reference  to  IV,  figure  63,  it  will  be  seen  that  the  refractive  power  is 
that  of  a  spherical  lens 

In  a  spherical  lens  the  power  is  the  same  in  all  meridians,  there  is 
no  need  therefore  to  designate  any  special  ones,  in  fact  it  would  be 
impossible  for  the  reason  that  they  are  all  alike.  In  the  cylindrical 
lens  they  are  not  similar,  the  power  of  the  lens  varies  in  each  meri- 
dian. For  purposes  which  will  be  seen  later  on,  it  is  found  necessary 
to  designate  the  meridians  in  which  the  greatest  and  least  power  (or 
rather  no  power)  obtains,  as  the  two  l^riucipal  meridians,  and  tliey  are 
alu-ays  at  right  angles  to  each  other. 


Figure  6j 


IS.     I,  llirough 
irough  axisol  c) 


■f  U.e  gee 
ical  lens; 


Cylindrical  lenses  are  convex  or  concave,  their  differences  being 
similar  to  the  difference  between  convex  and  concave  sphericals. 
Let  figure  64  represent  a  convex  cylinder,  it  will  be  seen  that  one  of 
the  principal  meridians  must  correspond  to  the  axis  X  S  and  the 
other  will  be  indicated  by  P  M  at  right  angles  to  it.  It  has  become 
customary  to  say  that  a  cylindrical  lens  has  two  axes,  a  major  and  a 
minor  axis.  This  is  correct, but  the  writer  frequently  finds  that  these 
terms  are  confusing  to  the  student  and  he  prefers  to  consider  f  at  the 
cylinder  possesses  but  one  axis,  viz: — that  meridian  in  which  no  re- 
fraction   occurs,    indicated  in  figure  64  by  X  S;  at  right  angles  to  the 


OCULAR 


REFRACTION. 


axis, in  the  meridian  where  the  greatest  refractive  power  of  the  cylin- 
der exists,  indicated  in  figure  64  by  P  M,  he  prefers  to  designate  it  as 
the  principal  meridian  of  the  cylinder;  a  definition  of  a  cylindrical 
lens  according  to  this  designation  is  as  follows: 


Figure  64. 

Convex  cylinder  lens  showing  varying  power  in  diffeient  meridians.      X  S,  the  axis;  P  M  (he 

principal  meridian. 

A  cylinder    lens  possesses    nncqual  pozvcr  of  refraction  in  7'irrions 
meridians;  in  the  plane  of  the  axis  no   refraction   occurs,  ivhile  at  right 


' 

] 

COS 

I 

B 

_D 

' 

\ 

I 

-\-2001, 

J 

Figure  05. 

Cross  sections  of  a  convex  cylinder  through   diiiferent  meridians.      1,  through   the  axi.s   V, 
through  the  principal  meridian;    II,  III  and  IV,  through  intermediate  meridians. 

angles  to  the  axis,  in  the  plane  of  the  principal  meridian,    the  greatest 
refraction  occurs. 


LENSES. 


63 


Cylindrical  lenses  are  numbered  in  both  the  inch  and  dioptric 
systems  the  same  as  spherical  lenses,  their  power  so  indicated  refers 
to  the  refractive  value  of  the  cylinder  in  its  principal  meridian.  Let 
figure  64  represent  a  convex  cylindrical  of  +  4.00  D.,  in  the  plane  of 
the  axis  its  power  is  O,  while  in  the  plane  of  the  principal  meridian 
the  power  is  +  4  00  D.  In  the  plane  of  a  meridian  A,  situated  equally 
distant  frcm  the  axis  and  the  principal  meridian,  the  power  is  one 
half,  or  +  2.00  D.;  in  the  meridian  B,  half  way  between  A  and  the 
principal  meridian  the  power  is  +  3  00  D. ;  in  the  meridian  C,  half 
way  between  A  and  the  axis,  the  power  is  +  i.oo  D. 

The  pozver  of  a  cylinder  increases  as  the  principal  lueridian  is 
approached  and  decreases  toward  the  axis. 


Figure  66. 


Parallel  rays  of  light   transmii 


by 


rposed  par 


This  will  be  explained  by  reference  to  figure  65.  I,  represents  a 
cross  section  of  the  cylinder,  figure  64,cut  through  its  axis,  A  Band  CD 
are  parallel  straight  lines;  II,  figure  65,  represents  the  cross  section  of 
the  cylinder  through  the-meridian  C,  figure  64, where  the  power  is  + 
1.00  D.  the  line  A  B  isstraight  while  C  D  is  slightly  curved;  III,  figure 
65  is  a  cross  section  of  the  cylinder  through  the  meridian  A,  the  power 
being  4- 2°o  D-  and  C  D  assumes  a  greater  curvature;  IV,  figure 
65  shows  a  cross  section  of  the  cylinder  through  the  meridian 
B,  figure  64,  the  power   being  -f  3  00  D.  the  curvature  of  C  D  is  still 


OCULAR 


R   K   F  R  A  C  T  I  O  N 


greater;  V,  figure  65  represents  the  cross  section  of  the  cylinder 
though  the  principal  meridian  with  the  power  +  4.00  D.  and  the 
greatest  curvature  to  C  D.  The  curvature  of  II,  III  and  IV  \s para- 
bolic. The  principal  meridian  alone  possessing  spnerical  curvature  it  is 
therefore  the  only  one  having  a  focus. 

The  focus  of  a  spherical  lens  is  a  point ;  the  focus  of  a  cylindrical 
lens,  if  we  can  so  term  it,  is  a  line.  Take  a  high  power  convex  cylin- 
der and  focus  the  light  upon  a  screen  in  a  similar  manner  to  the  pro- 
cedure with  a  spherical  lens,  and  there  will  appear  simply  a  bright 
line,  a  cylinder  /ciis  tlicrefore  docs  not  create  an  image,  in  proof  of  this 


look  at  a  round  spot  of  light  through  a  strong  convex  cylinder  and  it 
will  appear  as  a  strip  of  light,  being  distorted  from  its  real  form. 
This  is  the  principle  upon  which  the  "  Maddox  Rod  "  is  constructed ; 
it  will  be  described  later  on. 

Let  figure  66  represent  a  convex  cylinder,  before  it  is  placed  an 
opaque  disk  having  a  straight  slit  in  it,  the  slit  is  parallel  to  the  axis 
X  S  with  the  result  that  the  light  passing  through  the  slit  reaches  the 
screen  S  as  a  strip  A  B,  showing  that  in  this  meridian  no  refraction 
takes  place,  the  parallel  rays  emerge  from  the  lens  parallel  and  so 
reach  the  screen.      Such  an  opaque  disk  with  slit  as  that  illustrated  is 


.LENSES.  6s 

called  the  "Stenopaic"  disk  or  slit,  it  forms  a  very  valuable  aid  to 
diagnose  certain  conditions  of  refractive  error,  its  importance  is  too 
often  overlooked  and  by  many  not  even  understood  and  used. 

Figure  67  siiows  the  stenopaic  disk  the  slit  at  right  angles  to  the 
axisof  the  convex  cylinder,  the  parallel  rays  now  undergo  refraction  by 
the  principal  meridian  P  M  and  are  brought  to  a/oc/zsupon  the  screen 
S  to  a  point  A.  By  comparison  of  the  effects  illustrated  by  figures  66 
and  67  it  is  seen  that  when  the  stenopeic  slit  is  parallel  to  the  axis  of 
the  cylinder  it  destroys  its  power,  knowing  this  i^  is  always  possible  to 
locate  the  axis  of  a  cylinder  by  rotating  the  disk  before  it  and  noting 
the  meridian  in  which  no  refraction  occurs  and  objects  appear  the 
plainest.     The  explanation  of  this  phenomena  is  that  the  slit  cuts  out 


Light 


Figure  68. 

jfracted  by  a  convex  cylinder,  a  pin  hole  disk  imposed. 


all  rays  except  those  in  the  plane  that  is  parallel  to  the  opening;  or 
another  way  of  stating  it  is,  that  it  cuts  out  all  the  marginal  rays  ex 
cept  in  the  one  meridian. 

Figure  CS  represents  a  convex  cylinder  before  which  is  imposed  an 
opaque  disk  having  a  small  round  hole  in  the  centre,  it  is  called  the 
•'  Pin  hole  disk"  and  is  another  exceedingly  valuable  instrument  for 
purposes  of  diagnosing  refractive  errors.  By  reference  to  figure  17, 
illustrating  the  formation  of  the  image  of  a  candle  by  a  small  aperture, 
it  is  seen  that  this  gives  a  similar  effect.  The  cylinder  would  refract  the 
light  upon  the  screen  as  a  strip  but  the  pin  hole  cuts  out  all  but  a  few 


OCULAR 


REFRACTION. 


of  the  central  rays,  and  throws  a  small  round  spot  of  light  A  upon  the 
screen  S  which  is  not  very  bright  because  of  the  few  rays  transmitted. 
By  cutting  out  all  the  marginal  and  nearly  all  the  central  rays  the 
refractive  power  of  the  lens  is  destroyed  and  the  image  is  created  by 
the  pin  hole  alone  upon  the  principles  demonstrated  by  figure  17.  It 
will  be  recalled  that  the  size  of  the  image  created  by  the  aperture 
varied  with  the  position  of  the  screen  but  that  the  image  was  distinct 
in  all  positions.  In  the  same  way  the  pin  hole  shows  the  same  effects 
with  all  kinds  of  lenses,  convex  and  concave  sphericals  or  cylinders 
and  their  combinations.  The  student  should  experiment  to  prove  this 
until  it  is  clear  to  him  ;  take  any  kind  and  power  of  a  lens  from  the  test 
case,  hold  it  close  to  the  eye  and  endeavor  to  see  through  it,  no  matter 


the 


Figure  69. 

square  figure  as  seen  through  a  cone; 
appearing  the  longer  and  the  squ 


'lindncal  lens.    The  sides  parallel 
Decomes  a  parallelogram. 


how  indistinct  it  may  make  objects  appear,  when  the  pin  hole  disk  is 
imposed,  the  power  of  the  lens  is  destroyed  and  objects  are  clearly 
seen. 

Whenever  a  lens  possesses  unequal  curvature  in  various  meridians 
so  that  it  will  not  have  a  real  or  virtual  focus,  but  refracts  light  to  a 
line  (real  or  virtual),  it  is  said  to  be  an  astiginatit  and  the  optical  effect 
produced  is  called  astigiiiia  or  astigmatism.  The  name  is  derived  from 
the  word  stigma,  meaning  a  point;  astigmatic  meaning  no  point  or  focus 

Let  I,  figure  69  represent  a  square;  II,  represents  its  appearance 
viewed  through  a  concave  cylinder  axis  vertical.  The  square  becomes 
a  parallelogram,  the  longer  sides  being  parallel  to  the  axis  of  the  cylin- 
der; III,  shows  the  appearance  of  the  square   through  the  cylinder  the 


LENSES. 


67 


axis  being  horizontal,  now  the  lengthening  of  the  sides  is  in  a  horizon- 
tal direction.  If  a  convex  cylinder  be  used  to  make  this  experiment,  it 
will  be  found  to  distort  the  square  into  a  parallelogram  but  in  the 
opposite  direction,  the  sides  will  be  lengthened  parallel  to  the  principal 
meridian  and  at  right  angles  to  the  axis. 

The  cylinder  lens  illustrated  in  figure  69,  shows  one  of  the  custom- 
ary forms  of  a  lens  of  this  kind  used  in  the  test  case.  The  axis  is  indi- 
cated by  the  marks  X  and  S,  while  a  section  of  the  lens  on  each  side  is 
ground,  the  boundary  of  the  ground  surface  being  a  straight  line  par- 
allel to  the  axis. 


Figure  70. 


es  at  right  angles  to  eacli  other,  showing   that    they  are   equ 
to  a  convex  spherical  lens. 


Figure  70  represents  two  convex  cylinders  of  equal  power,  their 
piano  surfaces  together  and  their  axes  at  right  angles  to  each  other  It 
will  be  seen  that  the  principal  meridian  of  each  is  imposed  parallel  to 
the  axis  of  the  other;  by  combining  the  powers  of  each  of  the  parallel 
meridians  of  these  two  cylinders  it  is  found  that  the  strength  of  all  are 
alike,  and  as  this  complies  with  the  law  governing  spherical  lenses,  the 
two  cross  cylinders  in  this  position  have  a  convex  spherical  value. 
This  makes  possible  the  following  law:— 

A/iv  tii'o  like  (xlinJers  of  equal  power,  axes  at  right  angles  are  equal  to 
a  spherical  lens  of  the  same  power  and  kind.  Any  spherical  lens  may  be  con- 
sidered as  consisting  of  tic  0  cylinders  of  like  species  and  equal  power  whose  axes 
are  at  right  angles. 

A  clear  understanding  of  this  law  simplifies  calculations  in  com- 
bining lenses  of  various  kinds,  in  fact  any  cylinder  may  be  considered 
as  being  one  half  of  a  spherical  lens. 


O  C   I'   L  A 


KEF 


ACTION. 


Compound  lenses  are  divided  into  two  classes  or  species  accord- 
ing to  the  signs  indicating  the  character  of  tlie  curvatures 
involved       in      the      make      up      of       the       lens.  Combinations 

of  lenses  having  like  signs,  both  plus  or  both  minus,  are  termed  gt-iierif 
compounds;  while  if  the  signs  are  not  alike,  cne  plus  the  other  minus, 
they  are  known  as  co/it/a-gdieric.  Figure  70  represents  a  generic  com- 
bination. 

Combinations  of  cylinder  lenses  are  made  for  the  purpose  of  ob- 
taining certain  values  in  given  meridians,  it  is  therefore  necessary  to 
adopt  some  system  by  which  this  can  be  accurately  accomplished.  The 
circle  with  its  sub-division  into  three  hundred  and  sixty  degrees  was 
taken  as  the  basis.  A  horizontal  diameter  equally  divides  the  circle 
and  beginning  at  the  right  hand  side  it  is  marked  zero  (0°),  along  the 
circumference  upward  to  the  left  each  five  degrees  is  marked,  making 
the     vertical      meridian     ninety     (90),   to   the  left  of  the  vertical   and 


Figure  7  1. 

System  for  locating  the  axis  of  a  cylinder  in  tlie  trial   frame. 

downward  the  numbers  increase  until  the  horizontal  meridian  is 
reached  and  indicated  as  one  hundred  and  eighty  degrees  (180°).  Con- 
tinuing from  this  point  which  is  also  called  zero,  downward  and  to  the 
right,  the  numbers  increase  until  the  vertical  meridian  is  reached  and 
marked  (90°)  ninety  degrees  and  thence  around  to  the  starting  point 
which  is  indicated  as  one  hundred  and  eighty  degrees  (180°).  The 
vertical  meridian  is  always  indicated  as  90°,  while  the  horizontal  is 
called  180";  it  might  be  correctly  termed  zero,  but  the  other  designa- 
tion is  preferred.  Figure  71  represents  the  marking  of  a  trial  frame 
for  locating  the  axis  of  a  cylinder  according  to  the  above  system.    The 


LENSES. 


69 


reading  of  the  axis  indicated  by  the  trial  frame  is  made  by  the  observ- 
er as  he  faces  his  patient,  his  line  of  vision  thus  meets  the  outer  or 
anterior  surface  of  the  lens.  In  looking  through  a  lens  at  the  "  Pro- 
tractor scale  "  the  line  of  vision  meets  the  inner  or  posterior  surface 
of  the  lens.  This  explains  the  apparent  difference  in  the  positions  of 
the  numbers  of  the  trial  frame  scale  and  the    protractor    scale.  The 

vertical  and  horizontal  axes  read  the  same  on  both,  but  all  others  seem 
reversed,  thus;  Axis  45  degrees  on  the  trial  frame  appears  to  be  axis 
'35  degrees  on  the  protractor. 

A  spherical  and  a  cylinder  power  may  be  combined  in  one  lens,  in 
effect  it  is  a  combination  of  a  piano-spherical  and  a  piano-cylinder,  as 
the  spherical  curvature  is  ground  upon  one  surface  and  the  cylindrical 
curvature  upon  the  other.  The  spherical  and  cylindrical  curvature 
may  be  ground  upon  the  same  surface;  such  lenses  are  called  "Torus" 
or  "Toric."         They  have  a  noticeable  curvature,  similar  to  a  coquille 


.  Figure  72. 

Plano-convex  splierical  and  plano-convex  cylinder  combined;  showing  tlie  power  of  a  generic 
compound  in  its  principal  meridians. 

form,  an  J  within  certain  limitations  are  a  decided  improvement  over 
the  other  forms  in  both  appearance  and  satisfaction  to  the  wearer. 
They  give  a  wider  field  of  vision  and  are  free  from  annoying  reflection. 
The  thickness  of  the  lens  has  pfactically  little  effect  upon  the  optical 
value,  that  is  dependent    upon    the    curvature  of  the  surfaces. 

Let  I,  figure  72,  represent  a  piano  convex  spherical  of  2,00  D.;  II, 
represents  a  plano-convex  cylinder  of  i.oo  D.;  Ill,  represents  the  cylin- 
der in  combination  with  the  spherical,  its  axis  at  90°.  The  formula  for 
this  compound  will  be.- 

+  2.00  D.  S.  3  +  i-o^  ^-  Cyl.  ax.  90° 
and    it  will   be   classed    as  a  generic.     In    the   meridian   parallel  to  the 
axis  of  the  cylinder  the  power  of  the  combined    curvatures  will  be  that 


70  OCULAR         REFRACTION. 

of  the  spherical  alone,  while  in  the  meridian  parallel  to  the  principal 
meridian  of  the  cylinder,  the  power  will  be  that  of  both  the  spherical 
and  the  cylinder.  In  the  example  illustrated  by  figure  72,  the  power 
at  axis  90  is  +  2.00  D.;  at  axis  180°  +  3.00  D.,  the  cylinder  increasing 
the  power  of  the  spherical  at  this  meridian  its  full  strength. 

Let  figure  73  represent  a  contra-generic  compound,  the  spherical  a 
concave  of  4  00  D.,  the  cylinder  a  convex  of  3.00  D.  axis  45°;  it  should 
be  written: — 

— 4.00  D.  S.  3+  3'°°  D.  Cyl.  ax.  45°, 
The  power  of  this  combination  in  the  meridian  at  45°  is  —  4.00  D.  and 


Figure  73. 

A  contra-generic  combination  of  conve.x  cylinder  and  concave  spherical.      At  axis  45°,  the 

power  of  the  spherical  obtains;  at  axis  135°,  the  difference  between 

the  spherical  and  the  cylinder. 

in  the  meridian  at  135°  it  is  —  t.oo  D.,  it  has  at  least  —  i.oo  D.  power 
in  (vtry  meridian  and  this  can  be  subtracted  from  it,  for  a  —  i.oo  D. 
spherical  power  exists  in  the  combination.  If —  r.ooD.S.  besubtracted, 
in  the  meridian  at  45°,  —  3. 00  D.  remains,  while  in  the  meridian  at  135° 
no  power  remains.     The  formula  for  this   refractive  value  is  written: — 

—  I.oo  D.  S.  3  —  3°°  D.  Cyl.  ax.   135° 

which  is  a  generic  compound  and  is  the  optical  equivalent  of  the  origi- 
nal contra-generic  compound 

—  4.00  D.  S.  3  +  3°°  D.  Cyl.  ax   45°. 

From  this  it  will  be  observed  that  a  contra-generic  compound  can 
be  turned  into  a  generic.       The    process    of    converting  a  lens  formula 


from  one  form  into  another  of  equal  refractive  value  is  called  transposi- 
tion. 

The  subject  of  transposition  seems  always  to  have  been  a  more 
or  less  difficult  problem.  So  many  methods  may  be  followed  to  ac- 
complish the  same  resuls  that  they  have  called  for  various  rules,  more 
or  less  complicated  and  difficult  to  follow,  as  laid  down  by  various 
authorities.  Transposition  is  simply  a  matter  of  mathematical  cal- 

culation and  is  therefore  an  exact  proposition,  it  is  not  empirical  as 
many  seem  to  think  We  may  assume  that  the    piano    cylinder    is 

the  unit  and  once  its  principles  are  understood  it  is  no  longer  diffi- 
cult. An  endeavor  to  clear  the  subject  of  its  mystery  and  render 
it  as  simple  as  possible  will  be  made. 

Transposition  ii/ctriis  changing  the  form  [curvature)  but  not  the 
value  [dioptric  poiL'tr)  of  a  lens. 

A  comparison  may  be  drawn  between  changing  money  form 
without  altering-  is  value,  and  transposing  form  of  curvature  without 
altering  dioptric  power,  that  will  make  the  subject  clear.  A  dollar 
bill  may  be  changed  into  halves,  quarters,  dimes  or  pennies  ;  the 
value  of  the  dollar  has  not  been  altered  through  the  change  of  form. 
So  with  a  lens ;  its  curvature  may  be  changed  into  numerous  forms,  but 
so  long  as  the  relations  of  these  curvatures  to  each  other  are  undis- 
turbed, its  dioptric  power  remains  the  same. 

The  object  of  transposition  is  to  simplify  calculation  and  reduce 
the  cost  of  lens  making  ;  calculation  is  less  complex  with  simple 
formula.  If  a  desired  optical  effect  may  be  had  with  a  simple  and 
less  expensive  form  of  lens,  nothing  is  to  be  gained  by  using  a  more 
expensive  and  complicated  form.  There  may  be  cases  in  which  it 
is  desired  to  put  a  simple  into  a  more  complex  form  for  certain  rea- 
sons, as  in  using  torus  lenses. 

Transposition  of  spherical  formula  is  simple  ;  it  needs  no  further 
e,xplanatiori  than  that  already  given  in  a  previous  portion  of  this 
chapter,  that  the  dioptric  power  of  t  'e  spherical  (index  of  refraction 
of  course  being  the  same)  depends  upon  the  relation  of  the  curvature 
of  its  surfaces.  Figure  59  illustrates  three  forms  in  which  the  con- 
vex dioptric  power  is  the  same.  Figure  60  illustrates  four  forms  of 
concave  spherical  lens  in  all  of  which  the  dioptric  power  is  the  same. 

Transposition  in  which  cylindrical  power  is  involved  is  a  little 
more  complicated,  but  the  following  theorems  once  thoroughly 
understood  should  enable  the  student  to  take  up  the  subject  and  mas- 
ter it.  The  rules  are  simple  and  may  be  easily  interpreted  by  the  aid 
of  these  theorems. 

Theorem  I. — A.      T^vu  generic  cylinders  of  equal  power,    axes  at 


72  OCULAR  REFRACTION. 

r/;'///  (i/i£-/i:s,  arc  equal  to^a  spltcrical  of   tlic   same    iUoptric  power    ami 
species  as  one  of  the  cylinders. 
Examples  : 

+  i.oo  D.  C.  Ax.     90=  C  +  'oo  t3.  C.  Ax.   180'  =  +    1. 00  D.  S. 

—  2.75  D.  C.  Ax.  140,  C  —  2.73  D.  C.  Ax.    50°  =  —  2.7s  D.  S. 
+  1.50  D.  C,  Ax.     20   c  +  1.50  D.  C.  Ax.  110°  =  +   1.50  D.  S, 

—  0.50  D.  C.  Ax.     :o'  3  —  "-.so  D.  C.  Ax.  100'  =  —  0-50  D.  S. 

B.  Any  splicrical may  be  considered  as  tivo  generic  cylinders  of 
equal pozi'cr,  axes  at  right  angles. 

Examples  : 
.  —  2.00  D    S.  =  —  2.00  D.  C    Ax.  160°  C  —2.00  D.  C.  Ax.     70°. 
+  0,75  D.  S.  =  +  o  75  D.  C.  Ax.     85°  C  +  o  75  D-  C.  Ax.  175°. 

+  3.50  U.  S.  = 1-3  50  D.  C.  Ax.     50°  C  4-  3.50  D    C.  Ax.  (40°. 

4-  1.00  D.  S.  =  +  1.00  D.  C.  Ax.  115°  C  +  1.00  D.  C.  Ax      25  \ 

Tlicorem  II. — A.  Tivo  generic  cylinders,  axes  parallel,  are  equal 
to  one  cylinder  of  the  same  species  leliese power  is  that  of  the  tzco  com- 
bined, the  axis  will  be  the  sai/ic  as  that  of  the  original  cylinders. 

Examples  : 
+  1.25  D.  C.  Ax.  60°  C  +  0.50  D.  C.  Ax.  60°  =  +  1.75  D.  C.  Ax.  6c'. 
+  2.00  D.  C.  Ax.  25°C  +  1.50  D.  C.  Ax.  25'  =  +  3.50  D.C.  Ax.  25". 

—  0.75  D.  C.  Ax.i65°C  —  1.25  D.  C.  Ax.i65°  =—  2.00  D.  C.  Ax.i6s'. 

—  1.00  D.  C.  Ax    3o°3  —  °-7S  D-  D.  Ax.  30°  =  —  1.75  D.  C.  Ax.  30. 

/).  Any  cylinder  may  be  divided  into  two  generic  cylinders,  a.vcs 
parallel  to  the  original,  whose  combined  power  is  equal  to  that  of  the 
original. 

Examples  : 

—  3.00  D.  C  Ax.  20°=  —  1.25  D.  C.  Ax.  20°  C  --  1  75  D.  C.  Ax  20". 
+  1.50  D.C.  Ax.  95'=  +  1.00  D.  C.  Ax.  95°C  +  o  50  D.  C.  Ax.  95  . 
-\-  2.50  D.  C. Ax. 105"-    -f  1-75  D.  C.  Ax.io5°C  +  o  75  D.  C.  Ax.  105. 

—  2.00  D.  C.  Ax.  45=  —  1.00  D.  C.  Ax.  45°C  —  i  00  D.  C.  Ax    45". 

TheoreuiHI — Two  contragcnerie  cylinders,  axes  parallel,  are 
equal  to  one  cylinder  of  the  pozvcr  represented  by  the  difference  bctiveen 
the  tzvo,  the  axis  of  zv  hick  zvill  be  t  lie  same  as  that  of  the  originals  and 
its  sign  zvill  be  that  of  the  greater  If  they  are  of  equal  po:eer  they 

arc  equiz'alent  to  a  piano  glass. 


LENSES. 

Examples  : 
+  2.75  D.C.  Ax.     90  '  O  — 1.50  D.C.  Ax. 

—  3.25  D.C.  Ax.  i65°C  +1-75  D.C    Ax. 
-f  1.50  D.C.  Ax.     90°  C — 1. 50  D.C.  Ax. 

—  0.75  D.C.  Ax.  180°  C  +°-75  D.C.  Ax. 

Objective  demonstration  of  transposition  is  of  great  assistance  ; 
a  simple  system  of  diagrams  will  be  adopted. 

As  a  spherical  lens  possesses  equal  dioptric  power  in  every 
meridian,  it  may  be  represented  by  a  diagram  consisting  of  a  straight 
line  at  any  axis  crossed  at    right  angles    by    another    straight    line. 


90    =  +  1.25  D,C.  Ax.  90". 
I   5°= —  1.50  D.C.  Ax. 165°. 

90°  =  Piano. 

180°  =  Piano. 


Diagrammati 


Figure  74. 

epresentation  of  spherical  lenses.  I,  rt 
III,  +  3  50  D.  S.:  IV,  - 


.50  D. 


Figure  74  illustrates  spherical  values  by  diagrams.  I.    represents 

a+i.ooD.  S. ;  II.  represents  a — 2.00  D.  S. ;  II.  represents  a  + 
3.50  D.  S-;  IV.  represents  a  —  1.50  D.  S.  At  the  upper  and  right 
hand  ends  of  the  lines  the  dioptric  power  in  these  meridians  is  indi- 
cated. 

A  cylindrical  lens  may  be  represented  by  a  diagram  in  which  a 
straight  line  is  parallel  to  its  principal  meridian,  while  at  right  angles 
to  it  and  parallel  to  the  axis  of  the  cylinder  the  straight  line  is  crossed 
by  a  dotted  straight  line.  It  should  be  a  simple  matter  to  remem- 

ber this  by  comparing  it  to  the  saying — "united  we  stand,  divided  we 
fall  " — the  divided  or  dotted  line  represents  no  power  (the  axis),  the 
unbroken  line  represents  the  greatest  power  (the  principal  meridian). 


OCULAR 


REFRACTION. 


Figure  75  illustrates  c> Under  values  by  diagrams.  At  the  up- 
per and  right  hand  ends  of  the  lines  the  dioptric  power  in  these 
meridians  is  indicated ,  while    at    the  lower   and    left    hand    ends    is 


<fi>' 

Figure  75. 

!,  represents  a  +  2.00  D.  C.  ax.  90°; 
145°;  IV,  —  2.75  D.  C.  ax.  180.° 
epresents  no  power. 

marked  the  location  of  the  principal  meridians.  I.  represents  a  -|- 

2.00  D.  C.  Ax.  90°;  II.  represents  a  —  i.oo  D.  C.    Ax.    60°;    III.    repre- 
senis  a  +  1.75  D-  C.  Ax.  145°;  IV.  represents  a  —  2.75   D.  C.  Ax.    180°. 


iafjrammatic    representation   of  cv 

indrical  lenses 

il, -l.ooD.  C.ax.  ax.6o°;   U 

.  +  1.75  D.C. 

The  doited  line  ind 

cates  the  axis  a 

Figure  76. 

Diagram  to  represent  a  sphero  cylinder.   I,  represents  +  1.50  D.  C.  ax.  75°;  II,  4-  i  00  D.S.; 

III,  the  generic  sphe-'o-cylinder. 

To  represent  a  sphero-cylinder  lens  by  a  diagram,  it  will  be 
necessary  to  combine  the  diagram  representing  the  cylinder  with  that 
representing  the  spherical,  just  the  same  as  we  combine  spherical 
with  cylindrical  curvature  to  form  the  lens.  For  example,  take  the 
following  generic  compound  : 

+  1.00  D.  S.  C  +  '50  D.  C.  Ax.  75°. 


L  E  N  S  P:  S.  75 

First  draw  a  diagram  to  show  the  cylinder,  I,  figure  76;  then 
draw  a  diagram  of  the  spherical,  having  the  meridians  parallel  to  the 
principal  meridians  of  the  cylinder;  II,  figure    76.  If   these    were 

drawn  with  India  ink  upon  two  pieces  of  glass,  and  one   placed    upon 
the  other,  they  would  have  the  appearance  shown  by  III,    figure    76. 
The  unbroken  line  of  the  spherical  diagram  imposed  upon  the  dotted 
line  of  the  cylinder  diagram  makes  both  lines  appear  unbroken. 
+  0.75  D.  S.  C  —  2.00  D.  C.  Ax.  20°. 

Draw  the  diagram  of  the  cylinder  first,  representing  it  by  two 
unbroken  lines  (the  dotted  line  only  being  used  to  indicate  no  power, 
it  is  only  used  with  a  piano  cylinder).  Mark   the    power   and   the 

meridians,  then  indicate  the  spherical    power  on    the    same    diagram 
below  that  showing  the  cylinder  power,  see  figure  77. 


Figure  77. 
Diagram  to  represent  a  contra-generic  sphero-cylinder,  +  0.75  D.  S.  3  —  ~-°°  n.  C.  ax. 20° 

By  this  method  of  indicating  the  powers  mvolved,  the  value  of 
the  combination  in  the  principal  meridians  may  be  obtained  by  com- 
bining them.  Thus,  in  figure  77,  the  power  in  the  meridian  at  20°  is 
-f  0.7s  D.,  in  the  meridian  at  no'  it  is  —  1.25  D.  In  figure  76  the 
power  of  the  combination  in  the  meridian  at  75°  is  -f  i.oo  D.,  in  the 
meridian  at  165°  it  is  +  2.50  D. 

The  representation  of  cross  cylinders  by  diagram  will  be  simply 
that  of  two  piano-cylinders  imposed  upon  each  other;  the  lines  will 
obviously  be  unbroken,  the  marking  of  the  axes  and  powers  will  be 
similar  to  that  of  a  sphero  cylinder.  The  following  cross  cylinder 
will  serve  as  an  example,  illustrated  by  figure  78. 

+  I  00  D.  C.  ax.  175°  3  —  2.75  D.  C.  ax.  85°. 
I,  represents  the  first  cylinder,  the  convex;    II,   the  second  cylinder, 
the  concave;  III,  the  cross  cylinders. 


76  OCULAR         REFRACTION 

The  following  formulae  are  already  in  the  simplest  form.  Spher- 
icals,  piano  cylinders,  generic  spherocylinders,  and  contra-generic 
sphero-cylinders  in  which  the  cylinder  is  the  greater. 


Diagr; 


'  represent  cross 


Figure  78. 

I,  represents  tlie  convex   cylinder;    II,  the 
combination  of  the  two. 


A  contra-generic  sphero  cylinder,  in  which  the  spherical  power  is 
greater  than  that  of  the  cylinder,  may  be  reduced  to  a  generic  com- 
pound by  the  following  rule. 


Figure  79. 

Diagram  to    represent   transposition  of  a   contra-generic  sphero-cylinder  into  its  e([uivalent 
generic  sphero-cylinder. 

Rule  I. — Subtract  the  poivcr  of  the  cylinder  from  that  of  the  spher- 
ical, the  remainder  will  be  the  power  of  the  new  spherical;  the  pozccr  of 
the  cylinder  remains  the  same,  but  its  sign  changes  and  its  axis  loill  be 
at  right  angles  to  its  former  position. 

A  short  method  of  locating  the  new  a.xis  is  to  add  90^  if  the  origi- 
nal is  less  than  90",  or  subtract  90"  if  the   original    is  more  than  90". 


LENSES. 


Example:- 


+  3.50  D.  S.  C 
—  '25 


!SU.  c. 


•65° 

90 


+  2.25  D.  S.  C  +  1.25  D.  C.  ax    75° 

To  represent  this  by  diagram  let  I,  figure  79,  illustrate  the  origi- 
nal contra-generic  sphero  cylinder;  II,  figure  79  will  represent  the 
equivalent  generic  spherocylinder  which  may  be  divided  into  its 
component  spherical  and  cylinder  which  are  shown  by  III  and  IV, 
figure  79. 

A  contra-generic  sphero  cylinder  in  which  the  powers  are  equal, 
may  be  reduced  to  a  piano- cylinder  by  the  following  rule. 

Rule  IL — Arbitrarily  change  tlic  sign  of  the  cylinder  ami  locate  its 
axis  at  right  angles  to  its  former  position,  the  same  as  in  rule  I.  Drop 
the  spherical. 

Example: — 

+  1.50  D.  S.  C  —  1.50  D.  C.  ax.  180° 

9°;^ 

+  1.50  D.  C.  ax   90" 


Diagram   to  represent  transposition  of 


Figure  80. 

-gene 
piano  cylinder 


sphero-cylinde 


Figure  feo,  will  show  by  diagrams  how  this  is  done,  I,  represents 
the  sphero  cylinder;  II,  represents  the  piano-cylinder  resulting  from 
the  combination. 

Any  cross  cylinder  may  be  transposed  into  its  equivalent  sphero- 
cylinder by  the  following  rule. 

Rule  in. —  Take  either  cylinder  for  the  spherical.  Add  the  towers  of 
the  two  cylinders  to  obtain  the  power  of  tfie  new  cylinder,  its  a.\  is  and  sign  will 


O  C  U  LAR 


R   E   F   R   A   C  T  I  O  X 


!'c  ike  saute  as  the  original  cylinder  that  7C'as  not  converted  into  the  spherical. 
Example: — 

—  i.oo  D.  C.  ax.  180    3  +  1-5°  D.  C.  ax.  90° 
1.00  D.  C. 

—  1.00  D.  S.  O  "*"  2.50  D.  C.  ax.  90^ 
or  the  other  cylinder  be  made  the  spherical,   thus: — 

—  1.00  D.  C.  ax.  180°  3  +  '-5°  D.  C.  ax.  90" 
X-50  D-  C. 

—  2.50  D.  C.  ax.  i»o°  3  +  1-50  D-  S. 

This  may  be  represented  by  diagram;  let  I,  figure  81  represent 
the  cross  cylinders.       If  it  is  desired  to  make  the  convex  cylinder  the 


+I.SOII.  /So' 


Figure  81. 
Diagram  to  represent  transposition  of  cross  cylinder  into  its  equivalent  sphero-cylinder. 

spherical  it  will  be  necessary  to  add  +  1.50  D.  in  the  meridian  at  90", 
which  is  a  +  150  D  C.  ax.  180°,  this  is  shown  in  II,  figure  81.  Now  the 
addition  of  this  +  1,50  D.  in  the  meridian  of  90°  reduces  the  original 
so  that  it  must  be  increased  by  a  like  amount  to  offset  it.  We  there 
tore  add  —  1.50  D.  in  the  meridian  at  90',  which  is  —  1.50  D.  C.  ax. 
180°  and  is  shown  in  II,  figure  81.     Combine  these  powers  in  the  two 


LENSES.  79 

meridians  and  we  have  what  is  represented  by  III.  figure  8i.  This 
may  be  split  into  its  component  parts  shown  in  IV  and  V,  figure  8i. 

Any  sphero  cylinder  may  be  transposed  into  its  equivalent  cross 
cylinder  by  the  following  rules.      If  it  be  a  generic: — 

Rule  IV.—  TIte  spherical  bccouics  a  cylinder  tvitJiouf  cliangc  of  sign, 
its  axis  zi'ill  be  at  right  angles  to  that  of  the  original  cylinder.  The 
power  of  the  other  eylinder^icill  be  that  of  the  original  cylinder  and  the 
spherical  combined,  its  sign  and  axis  lall  be  the  same  as  the  original 
cylinder. 

If  the  spherocylinder  be  a  contra  generic,  in  which  the  cylinder 
is  greater  than  the  spherical : — 

Rule  V.  —  The  spherical  becomes  a  cylinder  ivithont  change  of  sign, 
its  axis  ivill  be  at  right  angles  to  that  of  the  original  cylinder-  The 
pozver  of  the  other  cylinder  :oi/l  be  the  difference  betiveen  the  pozvcrs  of 
the  spherical  and  original  cylinder,  its  'sign  and  axis  ivill  be  the  same 
as  the  original  cylinder. 


to  represent 


Figure  82. 

ansposition  of  a  spliero-cyl 


ito  Its  equival( 


indei 


If  the  sphero-cylinder  be  a  contra- generic  in  which  the  spherical 
is  the  greater,  reduce  it  by  Rule  I  to  a  generic  and  then  by  Rule  IV 
to  a  cross  cylinder. 

Example,  Rule  IV: — 

+  2.50  D.  S.  O  +  °-75  D'  C.  ax.  85° 

£:5^ 

+  2  50  D.  C.  ax.  175°  C  +  3-25  D.  C.  ax.  85° 
This  may   be   readily    explained   by   reference  to  theorem  I,  B; 
divide  the  spherical  into  its   equivalent   cross  cylinders  and  we  have 
+  2.50  D.  C.  ax.  175°  C  +  2.50  D.  C.  ax.  85°  C  +  0.75  D.  C    ax.  85° 


So  O  C   U   L  A   R  I<  E   F   r<   A  C  T  I  <)  N  . 

on  combining    the   two  parallel  generic  cylinders  we  have  the  result 
given  above. 

By  diagram  we   may  represent    the    transposition  in  figure  82 ;  I, 
shows  the  sphero-cylinder ;  II,  the  cross-cylinder. 
Example,  Rule  V: — 

+  1.25  D.  S  3  —  2.7s  D.  C.  ax.  40° 

';2S 

+  1.25  D.  C.  ax.  130°  3  —  jso  D.  C.  ax.  40° 
Divide  the  spherical  into  its  equivalent  cross  cylinders  as  above 
+  1.25  D.  C.  ax.  130°  C  +  1.25  D.  C.  ax.  40°  3  —  2.75  D.  C.  ax.  40° 


Figure  83. 


The  broken  appearance  of  a  vertical  straight  lin 
upon  lis  optical  centre.     I,  a  cc 


setn  through  a  piano-cylinder  lens  rotate 
ivex;  II,  a  concave  cylinder. 


and  then  combine  the  parallel  contra-generic  cylinder,  the  above 
result  will  be  obtained.  A  diagrammatic  representation  is  unnecessary. 
In  experiment  illustrated  by  figure  50.  it  was  found  that  upon 
rotating  a  spherical  lens,  a  vertical  straight  line  seen  through  it  was 
not  distorted;  this  property  serving  as  one  of  the  means  of  identifying 
a  spherical.  If  the  same  experiment  be  made  with  a  cylindrical  lens, 
the  line  will  appear  to  break  at  the  edges  of  the  lens  and  to  oscillate, 
swinging  to  a  certain  distance  and  then  back  again.  Figure  83  will 
illustrate  the  effect  created;  I,  shows  the  appearance  of  the  vertical 
straight  line  see  1  through  a  convex  cylinder;  II,  the  same  line  seen 
through  a  concave  cylinder.      Comparison  shows  that  the  direction  of 


LENSES.  8i 

the  motion  of  oscillation  is  the  reverse  with  a  convex  to  what  it  is 
with  a  concave.  In  making  this  experiment  it  will  be  noticed  that  in 
two  positions,  as  the  lens  is  rotated,  the  vertical  straight  line  will 
appear  unbroken  as  seen  by  A  and  B,  figure  84.  This  applies  to  both 
convex  and  concave  cylinders,  no  difference  in  them  will  be  detected 
if  each  be  placed  in  these  positions. 

In  the  illustrations  the  cylindrical  lenses  shown  are  purposely 
taken  from  the  test  cases,  to  make  it  as  easy  as  possible  for  the  stu- 
dent to  understand;  their  action  is  exactly  the  same  as  other  similar 
lenses. 


Figure  84. 

lliibroken  appearance  of  a  vertical   straight 
positions.     The  cylinder  r 

Mark  with  India  ink  at  the  edge  of  the  lens  the  four  points 
through  which  the  line  appears  to  pass,  unbroken,  this  procedure 
being  similar  to  that  in  experiment  illustrated  by  figure  47.  It  will 
be  found  that  these  points  are  90°  apart,  that  if  opposite  points  be 
joined  by  straight  lines,  these  lines  will  cross  each  other  at  right 
angles.  If  they  do  not,  erase  them  and  try  again  for  this  is  the  proof 
that  the  points  are  correctly  located. 

These  two  lines  -..•ill  iiidieate  the  two  piiiieil^a!  iiieriiUaiis  of  tlie 
cylinder,  an, I  their  point  of  interseetion  ivill  be  its  opiieal  centre. 

This  experiment  serves  a  double  purpose,  by  means  of  it  we  can 
identify  a  cylinder  and  locate  its  principal  meridians.  The  next  point 
is  to  determine  which  of  these  is  the  principal  meridian  and  which  the 


82  OCULAR         REFRACTION. 

axis.  Rotate  the  plane  cylinder  to  a  position  in  which  the  vertical 
straight  line  appears  through  it  unbroken;  by  reference  to  II,  figure 
48  the  effect  desired  will  be  seen,  the  line  passing  through  two  of  the 
points  marked  upon  the  lens.  With  the  lens  in  this  position  repeat 
experiment  illustrated  by  figure  4^5.  If  the  motion  of  the  lens  to  the 
right  and  left  causes  the  portion  of  the  lens  seen  through  it  to  move, 
breaking  and  causing  its  displacement,  refraction  must  take  place  in 
this  meridian.  Knowing  that  no  refraction  occurs  in  the  axis  of  a 
cylinder,  this  meridian  must  be  the  principal  meridian.  Connect  the 
two  points  marked  up  )n  the  lens  that  are  in  the  vertical  plane,  when 
the  lens  is  in  this  position,  with  a  line  of  dots  marked  with  the  india 
ink,  see  figure  85,  tin's  zvill  be  the  n.vis. 


Displacement 


If  the  motion  of  the  object  seen  through  the  lens  be  opposite  or 
against  that  of  the  lens,  the  cylinder  is  convex,  the  appearance  created 
is  shown  by  1,  figure  85.  If  the  motion  of  the  object  viewed  through 
the  lens  be  the  same  as  that  of  the  lens,  or  with  it,  the  cylinder  is  a 
concave  and  II,  figure  85  illustrates  the  effect. 

Now  rotate  the  lens  90'',  so  that  the  vertical  straight  line  also  ap- 
pears unbroken  and  passing  through  the  other  two  points;  move  the 
lens  to  the  right  and  left  as  before  and  the  line  as  seen  through  it  will 
not  appear  to  move.  No  refraction  occurs  in  this  meridian  and  this 
indicates  the  axis.  Figure  86  illustrates  this  experiment,  no  matter  if 
the  cylinder  be  convex  or  concave,  so  long  as  the  dotted  line  remains 


LENSES. 


83 


at  right  angles  to  the  vertical  line,  no  distortion  or  displacement  takes 
place.  The  effect  optically  is  that  of  piano  glass.  These  experiments 
demonstrate  the  fact  that  the  power  of  a  cylinder  is  at  right  angles  to 
its  axis. 

The  characteristics  of  a  piano  cylinder  lens  may  be  summarized 
in  a  few  words  as  follows: — 

First: — Upon  rotating  it,  objects  seen  through  it  appear  distorted. 

Second  : — In  two  positions  a  vertical  straight  line  appears  through 
it  unbroken,  in  each  position  the  line  is  parallel  to  one  of  its  principal 
meridians. 


A  vertical  straight 
angles 


jgh  various  portions  of  a  piano-cylinder  lens  its  axis  at  right 
The  cylinder  may  be  either  convex  or  1 


Third: — Motion  occurs  at  right  angles  to  one  of  these  meridians 
which  is  the  axis. 

Fourth: — If  the  motion  of  the  object  seen  through  it  is  against 
that  of  the  lens,  the  cylinder  is  convex;  if  it  is  concave  the  motion 
will  be  with  that  of  the  lens 

If  a  vertical  straight  line  be  viewed  through  a  prism  whose  base 
line  is  at  right  angles  to  it,  the  line  will  appear  unbroken,  no  matter 
through  what  portion  of  the  prism  it  is  seen;  see  II,  Figure  87.  If 
the  base  line-of  the  prism  be  parallel  to  the  line  it  will  appear  broken, 
that  portion  of  the  line  seen  through  the  prism  being  displaced  toward 
the  apex  of  the  prism ;  see  I,  Figure  87.     The  amount  of  displacement 


OCULAR         R   E  F 


A  C  T  I  O  N  . 


is  the  same  regardless  of  the  portion  of  the  prism  through  which  the 
line  is  seen. 

If  a  prism  be  combined  with  a  spherical,  cylinder  or  sphero-cylin- 
der  lens,  the  dioptric  properties  of  the  spherical,  cylinder  or  sphero- 
cylinder  remain  unaltered  except  that  the  prismatic  displacement 
occurs  with  the  other  optical  characteristics  of  the  lens.  To  prove 
this  take  any  convex  spherical  lens  from  the  test  case,  preferably  a 
high  power  (say  -|-  14  oo  D),    because  it  cr  ates  a  small  image,  and 


Figure  87. 

Showing  prismatic  displ 

focus  an  image  upon  a  white  cardboard  screen  of  some  object;  the 
picture  presented  through  a  window  is  always  convenient.  Having 
obtained  a  clear  sharp  image  impose  a  prism  before  the  spherical  and 
in  contact  with  it,  the  image  will  instantly  be  displaced  but  it  will 
still  be  sharp  and  clear,  showing  that  the  focal  power  of  the  spherical 
has  not  been  disturbed. 

It  may  be  a  bit  confusing  to  the  student  to  find  that  the  image 
is  displaced  toward  the  base  of  the  prism  in  making  the  above  experi- 
ment, but  if  he  will  stop  to  think  a  moment  he  will  understand  that 
this  is  correct.  In  looking  at  an  object  through  a  prism,  the  object 
appears  displaced  toward  the  apex,  because  the  light  rays  coming 
from  the  object  to  form  the  image  are  refracted  toward  the  base  of 
the  prism,  and  the  displacement  of  the  image  is  therefore  toward  the 
base. 


LENSES.  85 

Figure  88  represents  cross  sections  through  a  convex  sphero- 
prism  and  a  concave  sphero  prism. 

If  a  prism  be  combined  with  a  cylindrical  lens,  the  base  line  of 
the  prism  being  at  right  angles  to  the  axis  of  the  cylinder,  the  effect 
in  the  direction  of  the  line  of  the  axis  is  that  of  the  prism  combined 
with  a  piano  glass,  practically  that  of  the  prism  alone.  If  in  combin- 
ation with  a  cylindrical  lens  the  base  line  of  the  prism  is  parallel  to 
the  axis  of  the  cylinder,  the  effect  is  that  of  the  cylinder  with  the 
prismatic  displacement.  From  the  foregoing  it  should  not  be  difficult 
to  see  the  effect  of  a  sphero  cylinder  prism. 

Referring  to  figures  36  and  53  it  is  seen  that  convex  spherical 
lenses  are  in  effect  two  prisms  base  to  base,  while  concave  spherical 
lenses  are  two  prisms  their  apices    together.       Any    ray    except    that 


Figure  88. 

Cross  sections  of  sphero-prisms. 

passing  through  the  optical  centre  of  a  spherical  lens  is  subjected  to 
prismatic  action  ;  any  portion  of  such  a  lens  except  the  optical  centre 
therefore  possesses  prismatic  as  well  as  dioptric  power. 

The  importance  of  properly  centering  lenses  is  thus  demonstrated 
unless  it  is  desired  to  combine  prismatic  with  dioptric  value.  To 
obtain  this  combination  in  any  lens  it  is  simply  necessary  to  cut  the 
lens  so  that  its  optic  centre  is  displaced  from  its  geometric  centre  in 
a  certain  direction  and  to  a  definite  amount,  or  to  "  decentre  "  the 
lens  as  it  is  termed.     See  figure  52. 

If  power  of  a  certain  kind  is  obtained  by  decentration  it  is 
obviously  necessary  to  follow  some  method. 


86  OCULAR  REFRACTION. 

Prisms  are  now  numbered  in  what  are  termed  prism  dioptres. 
According  to  this  sj'stem  a  one  degree  prism  at  a  distance  of  one 
metre  (40  inches  or  one  dioptre)  creates  an  optical  displacement  of 
ten  millimeters.  A  one  dioptre  spherical  lens  decentred  ten  milli- 
meters is  equivalent  to  a  one  degree  prism  combined  with  tne  spheri- 
cal. As  a  spherical  has  equal  power  in  every  meridian  the  prism 
value  will  be  the  same  if  the  lens  is  decentred  in  any  direction.  From 
the  above  the  following  rule  may  be  adopted. 

A  dccentration  of  ten  uiilliiiictcrs  gives  as  many  degrees  of  pris 
viatic  power  as  the  lens  possesses  of  dioptrie  pozver 

Examples  : 

Millimeters  decentred. 


Dio 

ptres 

+ 

1. 00 

+ 

2  50 

— 

4  00 

+ 

5  00 

+ 

2.50 

Va 

ue. 

+ 

I  00 

D 

3 

1° 

Prs 

I  00 

D 

3 

1° 

Prs 

+ 

■2  5° 

1). 

3 

2-5 

Prs 

— 

4  00 

D. 

3 

2° 

Prs 

+ 

5  00 

D 

3 

5° 

Prs 

+ 

2.50 

D. 

c 

1° 

Prs 

xamples: 

Prism. 

Dioptres 

2° 

3D. 

1° 

4D. 

ir 

5D. 

2r 

6  D. 

4° 

2  D. 

A  short  method  to  ascertain  the  amount  of  dccentration  required 
of  any  lens  to  obtain  a  given  prismatic  value  is  to  multiply  the  num 
ber  10  by  the  prism  degree  required  and  divide  the  result  by  the 
dioptric  power  of  the  lens. 

Millimeters. 
X   2  =  20  -  3  =  6§ 

X  J  =  10  -;-  4  =  2^ 

X  1^=  15  -  5  =  3 
X  2i  =  30  -  6  =  5 

X  4  =  40  -;-  2  =  20 

Theoretically  there  is  no  limit  to  the  amount  of  decentration  but 
in  practice  it  is  not  possible  to  obtain  decentration  to  a  large  amount 
owing  to  the  limitations  of  the  size  of  the  "  uncut  lenses."  Reference 
to  Figure  52  shows  a  lens  of  33x37  millimeters  to  be  made  from  an 
uncut  lens  about  45  millimeters  square.  By  applying  a  rule  to  the 
drawing  it  will  be  seen  that  it  will  be  possible  to  decentie  the  lens 
only  about  4  millimeters  in  one  direction  or  about  6  millimeters  in  the 
other.  It  will  thus  be  seen  that  where  the  desired  lens  is  large  the 
amount  of  decentration  possible  will  be  small;  also,  that  where  the 
dioptric  power  is  weak,  but  little  prismatic  effect  may  be  obtained 
by  decentration  within  the  limits  of  the  average  uncut  lens. 


LENSES  87 

The  writer  has  often  been  asked  by  students — "  Is  it  just  the  same 
when  you  decentre  a  lens  to  get  a  prism  effect  as  if  the  prism  were 
ordered  ground  with  the  spherical?  "—the  impression  being  that  there 
must  be  some  difference.  To  clear  this  point  it  may  be  stated  that 
there  is  no  difference,  all  prismatic  power  is  the  same,  only  differing 
in  degree. 

The  statement  has  been  made  that  a  spherical  lens  may  be  decen- 
tred  in  any  direction  with  equal  effect,  but  this  cannot  be  true  of  a 
cylindrical  lens  because  of  its  unequal  power  in  various  meridians. 
Decentration  in  the  direction  of  the  axis  creates  no  prismatic  effect; 
along  a  line  at  right  angles  to  the  axis,  the  amount  of  prism  developed 
will  be  the  same  as  if  the  cylinder  were  a  spherical.  Decentration 
along  any  intermediate  meridian  will  develop  prism  power  propor- 
tional to  the  dioptric  power  through  that  meridian.  Reference  back 
to  the  fubject  illustrated  by  figure  64  will  make  this  plain. 

Estimation  for  decentration  of  sphero-cylinders  need  not  be  made 
difificnlt,  the  spherical  and  the  cylinder  may  be  considered  separately 
and  then  combined,  but  taken  together  it  is  not  a  complex  operation. 
A  few  pijints  only  are  involved. 

If  the  decentration  is  parallel  to  the  axis,  only  the  value  of  the 
spherical  is  involved,  no  matter  if  the  sphere  cylinder  be  generic  or 
contra  generic. 

If  the  decentration  be  at  right  angles  to  the  axis  and  the  lens  is 
a  generic  compound,  the  dioptric  power  involved  is  the  full  amount 
of  the  spherical  and  the  cylinder  combined. 

If  the  decentration  be  at  right  angles  to  the  axis  and  the  lens  is  a 
contra  generic,  the  dioptric  power  available  for  prismatic  effect  is  the 
difference  between  the  spherical  and   the  cylinder. 

If  the  decentration  be  in  a  direction  other  than  parallel  to,  or  at 
right  angles  to  the  axis,  estimate  the  power  of  the  cylinder  in  this 
meridian  and  add  it  to  the  spherical  if  the  compound  be  a  generic,  or 
subtract  it  if  the  compound  is  a  contra-generic. 


The  subject  of  neutralizing  lenses  has  practically  been  covered  in 
this  chapter.  The  student  has  learned  all  the  difficult  points.  The 
recognition  of  spherical  lenses,  and  the  determination  if  convex  or 
concave  is  understood.  Cylindrical  lenses,  the  location  of  their  axes 
and  determination  of  species  has  been  explained.  Sphero  cylinders 
and  their  characteristics;  prisms,  simple  and  in  combination  have 
been  explained   and   the   student  who    has  faithfully  followed  up  the 


88  OCULAR         REFRACTION. 

work  SO  far  outlined  need  fear  no  difficulty  in  recognizing  any  kind  of 
lens.  The  only  point  yet  unexplained  is  the  determination  of  the 
exact  dioptric  value  of  an  unknown  lens. 

The  treatment  of  the  subject  will  be  taken  up  merely  in  the  form 
of  a  review  which  will  include  this  last  point,  the  procedure  to  deter- 
mine the  character  and  power  or  powers  of  an  unknown  lens  will  be 
given 

To  neutralize  means  to  destroy  J^ozcer.  It  is  inferred  that  a  certain 
power  or  property  is  possessed  by  something  when  the  term  neutra- 
lize is  used,  to  which  by  the  act  of  neutralizing,  is  opposed  a  similar 
power  or  property  that  counterbalances  its  action.  To  neutralize  is 
thus  to  oppose  power  of  a  certain  kind  with  similar  power  operating 
in  an  opposite  manner  so  that  both  are  destroyed. 


{ 


Figure   S9. 


In  optics  we  have  lenses  that  possess  directly  opposite  powers, 
creating  opposite  effects,  viz:— those  lenses  that  converge  light  rays 
and  those  that  cause  them  to  diverge. 

To  neutralize  optically  we  oppose  convex  and  concave  poiiur  and 
destroy  both,  the  effect  being  that  of  piano  glass.  To  demonstrate  the 
theory  of  neutralizing  let  fiigure  89  represent  two  prisms  of  equal 
power  and  similar  form.  If  they  should  be  imposed  base  to  apex,  it 
will  be  seen  by  reference  to  III,  figure  89,  that  across  section  through 
would  show  the  surfaces  A.  B.  and  F.  E.  to  be  parallel  and  therefore 
the  optical  effect  would  be  that  of  piano  glass.  The  refractive  power 
of  each  is  destroyed  by  so  opposing  their   powers.       To  prove  this  by 


LENSES.  gg 

experiment  take  a  prism  of  any  power  and  look  through  it  at  a  verti- 
cal straight  line,  holding  the  prism  as  shown  by  I,  figure  87,  the  line 
will  appear  broken.  If  a  prism  of  equal  strength  be  now  imposed 
the  line  will  assume  its  unbroken  appearance. 

To  follow  this  line  of  investigation  further,  suppose  a  plano-con- 
vex lens  and  a  planoconcave  lens  of  the  same  index  of  refraction  and 
the  same  radius  of  curvature  be  imposed  with  their  curved  surfaces 
in  contact.  By  reference  to  figure  90  it  will  be  seen  that  one  fits 
exactly  into  the  other;  t  e  refractive  value  is  then  the  same  as  piano 
glass.  The  converging  power  of  the  convex  is  neutralized  by  the 
diverging  power  of  the  concave. 


Figure  90, 

Neutralizing  spherical  lenses. 

An  ocular  demonstration  of  this  may  be  made  by  repeating 
experiment  illustrated  by  figure  48,  using  a  convex  and  concave 
spherical  of  the  same  dioptric  power,  the  lenses  being  selected  from 
the  test  case  The  movement  created  by  the  convex  lens  will  be 
against  that  of  the  lens,  while  the  movement  created  by  the  concave 
will  be  with  that  of  the  lens.  ]V/icii  tlwy  art  imposed  and  there  is 
perfect  uentralizatiou  no  moveiiieiit  wi/l  be  uianifest. 

In  the  same  way  a  convex  and  a  concave  cylinder  lens  of  the 
same  dioptric  value  neutralize  when  they  are  imposed  with  their  axes 
parallel. 

The  following  is  a  simple  procedure  to  neutralize  lenses  in  a 
scientific  manner.  Hold  the  lens  with  both  hands  and  rotate  it  as 
described  and  illustrated  by  figure  50;  if  no  distortion  occurs  it  is  a 
spherical. 


go  OCULAR         REFRACTION. 

If  it  is  determined  that  the  lens  is  a  spherical,  move  it  laterally 
with  a  prnduliim  like  motion  as  illustrated  by  figures  4S  and  57,  and 
neutralize  with  a  spherical  of  the  opposite  kind 

If  on  rotating  the  lens  distortion  is  manifest,  the  lens  is  either 
a  sphero  cylinder  or  a  piano  cylinder  (possibly  a  cross  cylinder). 
The  fact  that  distortion  occurs  betrays  the  presence  of  cylindrical 
power  in  the  lens.  Locate  the  principal  meridians  and  determine  if 
it  is  a  piano-cylinder;  if  it  proves  to  be  a  cylinder  neutralize  it  with 
a  cylinder  of  the  opposite  kind,  placing  the  axes  parallel. 

If  the  lens  is  found  to  be  a  sphero  cylinder  determine  if  it  is  a 
generic  compound,  which  will  be  the  case  if  the  motion  created  is  the 
same  in  both  principal  meridians;  that  is,  against  the  motion  of  the 
lens  in  both  meridians,  or  with  the  motion  of  the  lens  in  both. 

If  the  lens  is  a  generic  spherocylinder,  neutralize  the  meridian 
of  least  power  first  with  a  spherical;  this  will  represent  the  spherical 
power  of  the  unknown  lens.  Now  turn  the  lens  at  right  angles  and 
neutralize  the  other  principal  meridian  which  will  be  the  cylinder. 

If  the  lens  is  found  to  be  a  contra-generic  sphero- cylinder,  as 
will  be  manifest  by  the  fact  that  the  movement  in  one  of  the  principal 
meridians  is  with  and  in  the  other  again^  t  the  movement  of  the  lens,  it 
will  be  necessary  to  determine  upon  which  surface  the  cylindrical  is 
ground.  If  the  cylindrical  is  of  high  power  there  will  be  no  difficulty 
in  recognizing  it ;  if  it  be  of  low  power  it  will  be  difficult  to  recognize  it 
by  the  appearance  of  the  surface.  A  lens  measure  will  be  the  simplest 
way  to  determine  the  point  or  a  straight  edge  placed  in  contact  with 
the  surfaces  will  show  which  surface  is  the  cylindrical.  Having  de- 
termined whether  the  spherical  is  plus  or  minus,  neutralize  the 
spherical  first  and  then  the  cylindrical. 

Prismatic  dis[)lAcement  is  neutralized  by  placing  a  known  power 
prism  in  opposition  to  the  unknown  so  that  no  displacement  occurs. 


CHAPTER     III. 

PHYSICAL  OPTICS. 

'"PHE  student  may  be  inclined  to  think  by  this  time  that  the  study 
■^  of  optics  is  a  "dry  and  u  interesting-  grind,"  basing  his  opinion 
upon  the  matter  contained  in  the  preceding  chapter.  It  is  the 
foundation  upon  which  his  optical  knowledge  must  be  built  and  the 
measure  of  his  success  will  be  in  direct  proporiion  to  his  ability  to 
calculate  lens  formulas.  A  thorough  knowledge  of  the  properties  and 
application  of  lenses  is  absolutely  necessary  to  secure  proficiency  in 
higher  optics.  Education  is  not  a  commodity  to  be  purchased;  it 
must  be  secured  by  individual  effort;  every  man  must  obtain  it  by  his 
own  work.  There  is  no  royal  road  to  optical  knowledge  any  more 
than  there  is  to  any  other.  We  see  men  who  have  had  exactly  the 
same  opportunities  in  the  same  college  accomplishing  far  different 
results.  Is  it  not  due  to  their  individual  efforts  ?  If  a  man  is  mentally 
lacking  in  capacity  for  certain  work,  or  it  is  not  congenial  to  him,  it 
is  better  he  should  turn  his  talents  in  another  direction  for  which  he 
may  be  fitted.  A  certain  amount  of  mathematical  knowledge  is 
required  in  the  practice  of  applied  optics  and  unless  the  preceding 
subjects  can  be  mastered  the  student  had  better  attempt  to  go  no 
further.  Encouragement  may  be  held  out  to  him,  however,  by  stat- 
ing that  the  "  dry  "  portion  of  the  study  has  been  passed,  that  which 
follows  will  hold  his  attention  because  the  experiments  will  prove 
interesting. 

Physiological  Optics  may  be  more  intelligently  studied  if  the  stu- 
dent be  familiar  with  Physical  Optics.  The  living  eye  cannot  be 
dismembered  that  its  errors  may  be  determined  and  their  correction 
supplied,  but  mechanical  optical  instruments  of  man's  construction 
may  be  taken  apart  and  their  constituents  separately  considered  We 
may  also  take  the  various  lenses  we  have  been  studying  and  construct 
devices  that  nearly  approach,  mechanically,  the  functions  performed 
by  the  eye  under  normal  conditions.  Abnormal  conditions  may  also 
be  created  in  the  same  way;  their  effects  may  be  noted;  their  correc- 
tion may  be  estimated  and  applied.  Equipped  with  the  knowledge 
thus  obtained,  the  student  is  prepared  to  take  up  the  deeper  subject 
of  Physiological  Optics 


92  OCULAR  R   E   F  R  A  C  T   I  O   X. 

That  poition  of  Physical  Optics  with  which  the  student  must 
become  familiar  is  that  which  relates  to  the  formation  of  real  images 
by  lenses.  It  is  repetition,  but  the  subject  is  of  sufficient  importance 
to  bear  repeating,  to  state  that  a  j-cal  optical  image  is  anc  tliat  may  be 
received  upon  a  screen.  It  is  created  by  a  cou-\\v  spherical  lens  zJhicIi 
brings  the  rays  of  liglit  from  every  point  upon  the  object  to  a  focus,  and 
a  screen  placed  at  the  exact  focal  point  of  the  lens  loill  rccc/i'c  the  image. 

It  has  been  demonstrated  that  of  tlie  various  forms  of  lens,  only 
convex  spherical  lenses  are  capable  of  creating  real  images;  also,  that 
they  possess  two  faults  that  seriously  interfere  with  the  formation  of 
correct  images,  viz: — spherical  and  chromatic  aberration.  To  over- 
come these  defects  and  make  possible  the  creation  of  perfect  images 
that  are  geometrically  correct  pictures,  it  is  necessary  to  resort  to 
various  devices;  these  are  called  refracting  systems. 

The  simplest  form  of  a  refr;icting  system  consists  of  a  convex 
spherical  lens  with  a  diaphragm.  A  diaphragm  for  a  refracting  sys- 
tem is  usually  a  metal  disk  having  a  round  hole  so  situated  in  the  disk 
that  its  centre  corresponds  to  the  optical  centre  of  the  lens  and  placed 
in  such  position, with  regard  to  the  lens,  that  it  permits  only  the  light 
rays  that  pass  through  the  central  portion  of  the  lens  to  reach  the 
screen.  By  reference  to  figure  44  it  will  be  seen  that  if  such  a  dia- 
phragm were  placed  behind  the  lens,  the  rays  that  pass  through  the 
marginal  portion  of  the  lens,  and  have  their  focus  at  G,  would  be  cut 
out,  and  if  a  screen  were  placed  at  F,  a  sharp,  clear  image  would  be 
created.  This  is  not  an  absolute  correction  for  the  spherical  aberra- 
tion but  for  the  purposes  of  this  book  it  goes  far  enough  in  explana- 
tion. 

Referring  to  experiment  illustrated  by  figure  5S  we  found  that 
light  undergoing  refraction  was  dispersed,  due  to  the  difference  of  the 
degree  of  deviation  of  the  various  rays.  Those  rays  forming  the  red 
end  of  the  spectrum  being  the  least  refrangible,  those  at  the  violet 
end  being  the  most  refrangible.  We  have  learned  that  the  index  of 
refraction  varies  for  different  substances,  and  this  is  also  true  of  glass 
of  different  compositions 

I'he  index  of  refraction  and  the  power  of  dispersion  for  all  kinds 
of  glass  are  not  proportional,  and  because  of  this  fortunate  condition 
it  is  possible  to  construct  a  refracting  system  that  is  corrected  for 
chromatic  aberration  or  is  achromatic. 

An  achromatic  lens  consists  of  a  convex  spherical  of  high  refract- 
ing power  with  low  dispersion,  combined  with  a  concave  spherical  of 
low  refracting  power  and  high  dispersion.     In  the  perfect  achromatic 


I 


PHYSICAL         OPTICS.  93 

the  amount  of  dispersion  of  the  two  lenses  forming-  the  combination 
is  equal,  but  being  of  contra  generic  character,  or  opposite  kind, 
they  neutralize.  The  refracting  power  of  the  convex  being  greater 
than  that  of  the  concave,  the  convex  predominates,  being  only  parti- 
ally neutralized,  thus  giving  convex  spherical  power  free  from  chro- 
matic aberration.  Now  by  the  addition  of  a  suitable  diaphragm,  a 
refracting  system  that  is  corrected  for  both  spherical  and  chromatic 
aberration  is  obtained. 

These  topics  of  aberration  in  lenses  may  seem  irrelevant  to  the 
study  of  ocular  refraction,  but  when  the  subject  of  Retinoscopy  is 
reached  it  will  be  found  that  they  have  an  important  bearing  upon  the 
subject.  In  order  that  a  clear  understanding  of  the  formation  of  real 
images  may  be  had,  the  student  is  urged  to  make  at  least  all  the 
experiments  given  and  as  many  more  as  may  be  suggested  by  his  own 
observations.  The  greatest  handicap  to  a  complete  and  thorough 
knowledge  of  refraction  has  been  that  there  was  too  much  theory 
taught  and  too  little  demonstration.  The  mind  has  been  taxed  with 
theoretical  practice  while  the  eye  and  the  hand  have  not  been  trained 
to  apply  it. 

Figure  2  represented  a  simple  scheme  to  demonstrate  that  light 
travels  in  straight  lines  always;  an  ordinary  cigar  box,  through  a  little 
ingenuity,  serving  all  the  purposes  of  more  elaborate  apparatus. 

Procure  a  similar  cigar  box  and  remove  the  top  and  one  end.  In 
the  centre  of  the  other  end  cut  a  hole  one  and  a  quarter  inches  in 
diameter,  taking  care  to  make  it  even  and  round.  The  lenses  in  the 
average  test  cases  now  in  use  are  one  and  a  half  inches  in  diameter; 
if  two  pins  are  driven  an  eighth  of  an  inch  from  the  edge  of  the  hole 
toward  the  bottom,  a  lens  from  the  test  case  resting  upon  them  will 
have  its  optical  centre  at  the  centre  of  the  hole.  Bend  the  pins  up- 
ward and  cut  a  portion  off,  leaving  them  in  the  form  of  two  small 
hooks  upon  which  the  lenses  may  be  placed  without  danger  of  fall- 
ing out  of  position.  Make  two  similar  hooks  of  pins  on  the  inner 
side  of  the  hole,  thus,  a  lens  may  be  placed  upon  either  or  both  sides 
of  the  aperture  in  the  end  of  the  box. 

Take  a  small  block  of  wood  about  half  an  inch  wide  and  a  little 
less  in  length  than  the  width  of  the  box,  cut  a  slot  in  it  in  the  direc- 
tion of  its  length  and  parallel  to  the  edges  of  the  block.  In  this  slot 
insert  a  piece  of  white  cardboard  similar  to  those  used  in  experiment 
illustrated  by  figure  2.  This  will  form  a  screen  to  receive  the  image 
and  should  be  free  to  slide  back  and  forth  easily  in  the  box.  For 
convenience  the  bottom  of  the  box  may  be  marked  off  in  inches  along 


q4  OCULAR         R  E   F   R  A  C   T  I  O  X. 

its  length,  beginning  at  the  end  where  the  lenses  are  placed. 

Take  a  +  8  oo  dioptre  lens  and  place  it  in  position  on  the  pins 
before  the  aperture,  move  the  screen  to  a  point  five  inches  from  the 
lens  and  direct  the  aperture  toward  a  window.  A  picture  (image)  will 
appear  upon  the  screen.  Move  the  screen  nearer  to  the  lens,  the 
picture  blurs,  it  is  out  of  focus  because  the  screen  is  nearer  to  the  lens 
t/iaii  the  focal  point.  Move  the  screen  more  than  five  inches  away 
fr<nn  the  lens:  again  the  picture  blurs,  the  screen  is  beyond  the  focal' 
point. 

If  the  same  experiment  is  made  with  a  -f  lo.oo  dioptre  lens,  the 
screen  must  be  placed  four  inches  away  to  obtain  a  clear  picture,  with 
a  -\-  5.00  dioptre  lens,  eight  inches  away.  //  is  tints  demonstrated  that 
to  obtain  a  clear  image  the  screen  must  be  situated  at  the  focal  point  of 
the  refracting  system.  If  a  diaphragm  is  placed  back  of  the  lens  it 
will  be  found  that  while  the  image  is  not  so  bright,  that  it  is  more 
sharply  defined. 

The  student  will  notice  that  the  image  created  by  the  ten  dioptre 
lens  is  smaller  than  that  created  by  tre  eight  or  the  five  dioptre  lens. 

The  greater  the  power  of  the  refracting  system,  the  smaller  ivill  be 
the  image  created  by  it. 

It  is  of  the  most  importance  that  the  optical  student  should  under- 
stand this  difference  in  size  of  the  images  of  the  same  object  created 
by  lenses,  or  refracting  systems,  of  different  power.  It  explains  the 
inability  to  accept  a  full  correction  for  the  error  of  refraction  in  a  pair 
of  eyes  in  which  there  is  a  marked  difference  in  the  refraction.  It 
also  explain  why  it  is  frequent  to  find  in  such  cases  that  vision  in  one 
eye  is  much  poorer  than  the  other. 

Too  rnuch  experimental  work,  along  the  lines  given  in  this  chap- 
ter, cannot  be  done. 

Another  and  more  important  series  of  experiments  will  now  be 
given.  Move  the  screen  to  ten  inches  from  the  aperture  and  place  a 
+  2.00  D,  lens  before  it,  the  image  formed  upon  the  screen  will  be 
much  blurred.  Add  a  +  i.oo  D.  lens  and  the  image  will  appear  more 
clearly  defined,  but  still  far  from  perfect;  upon  adding  a  -|-  2  00  D. 
lens  to  the  original  it  will  he  found  that  the  image  is  now  clear. 
Substitute  for  the  two  -|-  2  00  D.  lenses  a  -\-  4.00  D  lens  and  the 
image  will  appear  the  same  as  though  created  by  the  two  +  2.00  D. 
lenses  combined.  Move  the  screen  to  five  inches  from  the  aperture 
an.  place  a  -(-  5.00  D.  lens  before  it,  the  image  will  not  be  clear. 
Trying  the  addition  of  convex  lenses  it  will  be  found  that  a  +  3  0°  D. 
will  be  required  to  make  the  image  clear. 


PHYSICAL         OPTICS.  95 

With  the  screen  placed  four  inches  from  the  aperture  and  a 
-|-  8.00  D.  lens,  -f  2.00  D.  must  be  added. 

If  the  screen  be  located  ten  inches  from  the  aperture  and  a  -f 
5  00  D.  placed  before  it,  the  image  will  be  blurred;  the  addition  of 
convex  lenses  renders  the  image  less  distinct.  By  adding  a  —  i.oo 
D  lens  the  image  will  be  rendered  clear  and  sharp.  Place  the  screen 
at  eight  inches,  and  using  a  -|-  8  00  D  lens,  it  will  be  found  necessary 
to  add  a  —  3  00  D.  lens  in  order  to  obtain  a  clear  image.  In  making 
these  experiments  then,  if  it  is  found  that  the  image  is  blurred  or  in- 
distinct, add  a  f('//rr.r  .f/'/zcr/ri'r/Av/.fTfrj-//  if  this  is  found  to  improve 
the  image  it  proves  that  more  refraction  is  required.  If  the  addition 
of  convex  lenses  make  the  image  less  distinct  concave  spherical  lenses 
are  indicated  to  neutralize  a  portion  of  the  refraction. 

From  the  above  the  following  rules  inay  be  given  : 

//  the  screen  Is  too  near  tlie  refracting  system  a  convex  lens  must  be 
added  to  create  a  clear  image. 

If  the  screen  is  too  far  from  the  refracting  system  a  concave  lens 
must  be  added  to  create  a  clear  image. 

Suppose  a  +  6.50  D.  lens  be  placed  at  the  aperture  and  ilie 
screen  moved  to  the  proper  position  to  secure  a  clear  image,  the  lens 
may  be  rotated  about  its  optic  axis  withe  ut  in  any  way  affecting  ih; 
image  ;  in  fact,  while  the  lens  is  in  motion  no  change  or  movement 
will  appear  in  the  image.  This  experiment  may  be  repeated  with 
any  power  lens,  the  result  will  be  the  same,  thus  : 

Any  convex  spherical  lensjoca/cd  at  the  proper  point  to  create  a  dis- 
tinct tillage,  may  be  rotated,  ictt/ioiit  o/h,'r-uw'se  a/tcrii?g  its positiomoitli 
regard  to  the  screen,  and  the  rotatiuu  icUl  not  affcit  the  image  because  of 
the  equal  refractive poioer  of  the  lens  in  every  meridian. 

The  device  used  in  the  above  experiments  is  in  eflfect  a  rude 
camera.  One  of  the  most  valuable  aids  to  the  study  of  physical  and 
physiological  optics  is  the  camera  obscura.  They  may  be  obtained  at 
a  small  cost,  about  a  dollar  each.  By  moving  the  lens  in  the  focus- 
ing tube,  an  out  of  focus  condition  may  be  created,  which  may  be 
corrected  by  imposing  the  necessary  convex  or  concave  spherical  lens. 
In  the  camera  obscura  the  image  is  formed  upon  the  ground  glass  on 
the  top,  the  light  rays  being  reflected  from  a  horizontal  to  a  vertical 
direction  by  a  mirror  placed  at  an  angle  of  forty  five  degrees.  This 
renders  observation  of  the  image  more  convenient. 

If  the  device  described  in  the  previous  experiments  be  used  to 
focus  the  rays  from  a  distant  luminous  point,  the  following  pheno- 
mena will  be  noticed.     When  the  screen  is  situated  at    the    principal 


96  OCULAR         REFRACTION. 

focus  of  the  refracting  system,  the  light  from  the  luminous  point  will 
be  focused  to  a  point  upon  the  screen.  If  the  screen  be  moved 
toward  the  refracting  system,  \.\\&  point  will  take  the  form  of  a  circle  of 
i//^//jtvz' //<,''/;/ upon  the  screen,  which  will  increase  in  size  the  nearer 
the  screen  is  approached  to  the  refracting  system.  If  the  screen, 
being  located  at  the  principal  focus,  is  moved  away  from  the  refract- 
ing system,  the  point  will  also  assume  the  form  of  a  circle  of  diffused 
light  upon  the  screen,  which  will  increase  in  size  the  further  the 
screen  is  removed. 

From  the  foregoing  experiments  it  has  been  demonstrated  that: 
Provided  convex  spherical  curvature  exists  a  focus  is  ohtainalde,  and  an 
image  may  be  created,  by  locating  the  screen  at  the  f.cal  point  of  the  sys- 
tem. 

In  Chapter  II.  on  lenses  it  was  explained  that  a  cylinder  lens, 
having  no  focus,  could  not  create  an  image. 

Repeat  the  hist  experiment  given,  using  a  -f  8.00  D.  spherical 
anda-(-  4.00  D.  cylinder  in  combination.  The  image  of  the  luminous 
point  upon  the  screen  will  not  be  a  point.  If  the  axis  of  the  cylinder 
is  in  the  horizontal  plane  and  the  screen  is  placed  close  to  the  refract- 
ing system,  the  circle  of  diffusion  shown  in  the  previous  experiment 
will  be  replaced  with  an  oval  spot  of  light  in  which  the  longest  dia- 
meter is  in  the  horizontal  direction.  As  the  screen  is  moved  away 
from  the  system,  the  oval  becomes  first  a  horizontal  streak  of  light, 
then  a  vertical  streak  and  finally  an  oval  spot  in  which  the  longest 
diameter  is  in  the  vertical  direction. 

If  the  axis  of  the  cylinder  should  be  placed  in  the  vertical  plane, 
and  the  screen  located  close  to  the  system,  the  oval  of  light  will  ap- 
pear with  the  longest  diameter  in  the  vertical  direction.  Upon  mov- 
ing the  screen  away  the  sti'eak  will  first  appear  vertical,  then  hori- 
zontal and  afterwards  change  to  an  oval  spot  having  the  longest 
diameter  horizontal. 

These  experiments  with  sphero-cylinder  lenses  show  that  the 
image,  if  such  it  may  be  called,  is  distorted  and  blurred,  therefore  : 

When  uneijual  curvature  exists  no  focus  is  obtainable,  and  no  image 
^c'ill  be  created,  no  matter  7vhat  the  location  of  the  screen. 

It  has  been  demonstrated,  and  the  student  by  this  time  is  doubt- 
less sure,  that  a  spherical  lens  possesses  equal  refracting  power  in 
every  meridian.  If  some  method  can  be    devised    to    determine    if 

any  given  refracting  system  does  possess  equal  refraction,  and  there- 
fore curvature  in  every  meridian,  such  determination  being  based 
upon  an  ocular  demonstration  by  which  it  will  be    possible    to  actually 


PHYSICAL         OPTICS.  97 

^f^  the  effect  created,  it  will  readily  be    understood  how  important  it 
would  be. 

To  accomplish  this  the  familiar  clock  dial  geometrical  figure  was 
devised,  also  the  fan  dial,  which  is  one  half  of  the  clock  dial.  These 
are  known  as  astigmafic  test  charts. 

In  these  charts  the  series  of  three  parallel  lines  radiate  from  a 
centre;  the  lines  are  all  of  equal  length,  width  and  blackness,  while 
the  spaces  between  each  of  the  parallel  lines  are  of  the  same  width  as 
the  lines. 

An  image  of  the  astignuitic  test  figjirc.  erealed  hv  a  refracting  sys- 
tem liaving  equal  refraction  in  every  meridian,  ivtll  show  every  line 
equally  distinct. 

.  Ii  the  refraction  is  unequal  in  various  meridians,  the  focal  length 
of  the  different  meridians  varies,  and  the  screen  cannot  be  placed  in 
any  position  to  receive  the  image  of  all  the  various  series  of  lines. 
The  screen  being  placed  to  receive  a  clear  image  of  the  lines  in  one 
meridian,  those  in  the  other  meridians  will  appear  more  or  less  indis- 
tinct, because  they  are  out  of  focus. 

An  image  of  the  astigmatic  test  figure .  created  by  aiiv  refracting 
system  in  loiitch  t lie  refraction  is  unequal  iii  rarious  mc'iidiaiis.  wi'll 
show  the  series  of  lines  of  unequal  I'laikacsi  and  some  less  dntinct  than 
others. 

Therefore,  if  any  refracting  system  creates  an  image  of  an  astig- 
matic test  figure  in  which  the  Imes  do  not  all  appear  alike,  it  demon- 
strates that  the  system  has  not  true  spherical  refraction,  in  other 
words,  that  it  is  astigmatic. 

The  astigmatic  test  figure  makes  an  excellent  object  of  which  to 
create  an  image,  and  if  such  image  shows  some  or  all  of  the  lines  out 
of  focus,  lenses  may  be  imposed  until  all  the  lines  appear  alike  and 
distinct.  Use  the  cigar  box  device  in  the  experiments,  or  by  placing 
a  cylinder  lens  behind  the  spherical  lens  of  the  camera  obscura,  it 
may  be  made  astigmatic.  A  couple  of  bent  pins  will  serve  to  support 
the  cylinder. 

Suppose  all  the  lines  of  the  figure  originally  appeared  blurred,  if 
the  addition  of  convex  spherical  lenses  causes  them  to  become  less 
distinct,  try  concave  sphericals.  If  all  the  lines  can  be  brought  out 
equally  clear  and  distinct  with  either  convex  or  concave  sphericals,  it 
will  show  that  the  refracting  system  possessed  too  much  or  too  little 
refracting  power  consistent  with  the  position  of  the  screen. 

If  at  the  beginning  it  is  seen  that  the  lines  in  some  one  meridian 
are  clear  and  the  others  blnrred,  a  plane  cylinder   will  be  required  to 


qS  O  C   I'   L  A  R         R   K   F    R  ACTIO   X. 

correct  the  astigmatic  error  in  the  refracting  system.  It  has  been 
demonstrated  that  the  two  principal  meridians  are  always  at  right 
angles  to  each  other,  therefore: — 

If  tlic  lines  in  one  meridian  appear  tJie  most  distmet,  those  in  the 
meridian  at  riglit  angles  ivill  appear  the  most  blurred. 

The  axis  of  the  correcting  cylinder  will  be  found  to  be  parallel  to 
the  meridian  in  which  the  lines  appear  the  most  indistinct;  an  easy 
rule  to  remember  will  be  to: 

AkiHiys  place  the  axis  of  the  cylinder  at  right  angles  to  the  blackest  lines, 
this  applies  if  the  cylinder  be  either  convex  or  concave. 

If  all  the  lines  appear  indistinct,  but  some  more  so  than  others, 
use  convex  or  concave  sphericals  as  may  be  necessary  until  the  lines 
in  some  one  meridian  are  clear  and  distinct,  then  proceed  as  in  the 
case  where  a  plane  cylinder  was  required. 

Astigmatism  is  always  created  where  the  curvature  is  unequal  in 
the  various  meridians,  the  refraction  being  unequal;  it  may  occur  also 
when  the  curvature  is  equal  in  all  meridians  by  inclining  the  lens  at 
such  an  angle  to  the  incident  rays  that  they  undergo  unequal  refrac- 
tion. This  is  due  to  the  same  phenomena  that  creates  spherical  aber- 
ration and  is  called  astigmatism  by  incidence. 

With  a  strong  convex  spherical  lens,  say  ten  dioptre,  create  an 
image  upon  a  screen,  the  lens  and  screen  both  being  in  a  vertical 
position.  If  the  lens  be  tilted  obliquely  the  image  will  immediately 
become  blurred  and  less  distinct  the  greater  the  inclination  of  the 
lens.  It  is  caused  by  the  astigmatic  condition  created  by  the  lens  in 
this  position. 

Persons  wearing  high  power  lenses  experience  annoyance  through 
this  phenomena  if  the  lenses  are  not  properly  "  set  "  before  the  eyes. 
Reading  glasses  should  be  tilted  forward  at  the  top  to  overcome  this 
defect,  the  angle  to  be  determined  by  experiment  for  each  particular 
wearer. 

The  most  perfect  instrument  of  mechanical  construction  for  the 
formation  and  recording  of  optical  images  is  the  modern  photographic 
camera.  It  may  be  said  to  duplicate  the  functions  of  the  human  eye 
in  everything  except  the  ability  to  record  color.  It  is  capable  of  record- 
ing the  intensity  of  light  and  may  therefore  be  said  to  be  possessed  of 
the  light  sense.  When  equipped  with  a  pair  of  matched  lenses,  for  the 
making  of  stereoscopic  photographs,  it  may  be  said  to  have  the  power 
of  recording  form  and  therefore  has  the  form  sense.  It  is  within  the 
range  of  possibility  that  the  color  sense  may  be  added  within  a  short 
time.       The  refracting  system  is  corrected    for    chromatic    aberration 


P  II  V  S  I  C  A  L         OPTICS.  99 

and  it  is  now  possible  to  obtain  a  true  achromatic  lens,  which  is  more 
than  can  be  said  for  the  human  eye. 

The  iris  diaphram,  so  called  for  its  resemblance  to  the  iris  of  the 
eye  in  its  action,  corrects  the  spherical  aberration.  The  bellows  per- 
mits of  the  focussing- of  the  lens  for  all  distances;  in  this  respect  it 
corresponds  to  the  power  of  the  eyes  to  accommodate  for  different 
distances.  In  the  camera  the  distance  between  the  refracting  system 
and  the  screen  is  changed.  In  the  eye  the  power  of  the  refracting 
system  is  changed,  the  relative  position  of  the  screen  and  the  refract- 
ing system  being  unchangeable. 

In  the  steroscopic  camera,  two  lenses  having  exactly  the  same 
refracting  power  are  used  to  make  two  separate  pictures  of  the  same 
subject  upon  the  same  plate,  side  by  side.  The  two  lenses  corres- 
ponding to  the  two  eyes  of  a  person,  the  line  ot  vision  for  each  being 
directed  to  the  same  object. 

Stereoscopic  pictures  seem  to  be  two  pictures  of  the  same  subject 
exactly  alike  in  every  detail,  but  such  is  not  the  case.  By  reason  of 
the  distance  between  the  lenses,  corresponding  to  the  average  dis- 
tance between  the  two  eyes  of  a  person,  two  different  view- points  are 
obtained  and  a  slight  difference  in  the  pictures  occurs.  In  each  of  the 
pictures  will  be  found  some  objects  that  do  not  occur  in  the  ether, 
some  that  are  missing.  This  duplicates  the  function  of  binocular 
vision,  that  is,  single  vision  with  two  eyes,  the  two  images  fusing  or 
blending  into  one. 


CHAPTER  IV. 
PHYSIOLOGY  AND  ANATOMY. 

NO  treatise  upon  the  refraction  of  the  eye  would  be  considered 
comprehensive  or  complete  that  did  not  embrace  the  physiology 
and  anatomy  of  the  eye,  so  that  the  writer  feels  it  is  necessary 
to  devote  a  chapter  to  the  subject.  No  attempt  will  be  made  to  write 
an  authorative  paper,  nor  will  it  be  the  aim  to  elucidate  any  new  facts; 
too  many  text  books  have  been  written  upon  the  subject,  by  far  abler 
writers,  to  which  the  student  is  referred  for  fuller  information  than  it 
is  necessary  to  incorporate  in  this  work.. 

The  medical  refractionist  so  frequently  accuses  the  non-medical 
refractionist  with  lack  of  knowledge  of  the  functions  of  the  eye,  and 
upon  this  lack  of  knowledge  condemns  his  ability  to  correctly  estimate 
and  prescribe  for  refractive  errors,  that  it  behooves  one  to  be  as  well 
informed  as  possible,  to  be  able  to  talk  to  a  patient  as  intelligently 
upon  the  subject  as  his  competitor. 

The  sense  of  sight  is  not  the  result  of  a  purely  mechanical  phe- 
nomena like  the  making  of  a  photographic  image  with  a  camera,  for 
it  involves  certain  complex  physical  functions  of  each  eye  separately 
and  working  in  unison.  There  must  be  a  harmonious  action  of  the 
two  eyes  so  that  perfect  binocular  vision  may  exist. 

In  order  that  the  ocular  refractionist  may  do  justice  to  his  patient, 
and  credit  to  himself,  he  must  understand  the  fundamental  facts  of 
the  anatomy  of  the  eyes  and  how  they  perform  their  functions. 

This  cnapter  is  made  up  largely  of  matter  taken  from  the  writ- 
ings of  well  known  authorities,  with  such  explanations  as  the  writer 
is  able  to  give  in  order  to  simplify  the  statements, which  were  origin- 
ally intended  for  the  use  of  medical  students,  an  effort  to  give  them 
in  simpler  language  will  be  made. 

It  is  a  well  known  fact  that  in  order  to  obtain  as  extended  a  field 
of  view  as  possible  it  is  necessary  to  seek  an  elevation, one  climbs  to  the 
top  of  a  hill  in  order  to  see  as  far  as  possible.  Upon  this  principle 
Nature  locates  the  eyes  in  the  upper  portion  of  the  head,  the  skull 
being  the  most  elevated  portion  of  the  human  frame;  thus,  the  advan- 
tage of  position  to  secure  a  comprehensive  view  is  obtained. 


PHYSIOLOGY        AND         ANATOMY.  loi 

The  next  important  fact  noticed,  is  the  protection  afforded  the 
eyes,  by  the  bony  cavities  in  which  they  are  placed.  These  are  called 
the  sockets  or  ^r^/V.j  of  the  eyes  and  are  in  the  form  of  an  irregular 
cone  or  four  sided  pyramid,  the  apex  being  inward.  The  aperture  of 
the  orbit  is  larger  than  the  diameter  of  the  eye,  being  about  one  and 
three-eights  of  an  inch  in  diameter,  while  the  eye  is  about  an  inch  in 
diameter.  The  space  between  the  eye  and  the  bony  walls  of  the  orbit 
is  filled  with  cushions  of  fat  that  serve  as  further  protection, and  upon 
which  the  eye  rotates  freely.  The  principal  opening  into  the  orbit  is 
at  its  apex,  through  which  the  nerve  of  sight,  the  optic  ticrvc  reaches 
the  brain.  The  axes  of  the  orbits  are  not,  as  would  naturally  be  sup- 
posed, parallel,  but  converge  toward  the  centre  of  the  skull. 

A  further  protection  is  afforded  the  eyes  by  the  eyelids,  which 
close  together  tightly  and  involuntary  whenever  any  object  is  brought 
dangerously  close  to  the  eye.  The  edges  of  the  eyelids  are  furnished 
with  a  thick  row  of  short  hairs  that  serve  to  ward  off  small  particles 
of  foreign  bodies,  such  as  dust,  cinders,  etc. 

In  connection  with  the  eyelids  may  be  considered  the  lacliryuial 
organs  that  serve  to  keep  the  surface  of  the  eye  moist.  If  any  small 
particles  reach  the  surface  of  the  eye,  a  copious  flow  of  lachrymal  fluid 
or  fears  washes  away  the  offenders,  as  the  eye  is  extremely  sensitive 
to  the  presence  of  any  foreign  substance,  a  small  cinder  or  any  rough 
particle  will  set  up  a  serious  inflammation  in  a  very  short  time. 

The  eye  is  spherical  in  form  and  aboiit  one  inch  in  diameter,  up- 
on its  outer  surface  is  a  section  of  a  smaller  sphere  which  increases  its 
antero  posterior  diameter.  This  small  sphere  is  attached  to  the  larger 
in  much  the  same  manner  as  the  crystal  is  attached  to  an  open-faced 
watch.      The  axes  of  the  eyes  are  parallel  to  each  other. 

The  eye  is  composed  of  three  ineinbranes  that  enclose  the  refract- 
ing media  or  humors  The  membranes  are  the  Sclerotic,  the  Choroid 
and  the  Retina.  The  humors  are  the  Aqueous,  the  Crystalline  Lens 
and  the  Vitreous. 

The  outer  membrane  is  the  sclerotic  and  is  a  tough  fibrous  mem- 
brane that  gives  form  to  the  eye,  it  is  what  is  commonly  called  the 
"  white  of  the  eye."  The  Cornea  is  a  part  of  the  sclerotic,  forming 
about  one  filth  of  its  area,  and  is  transparent.  Looking  at  an  eye 
obliquely  the  form  of  the  cornea  may  easily  be  seen  elevated  above 
the  larger  sphere  of  the  eye.  The  form  of  the  cornea  is  similar  to  a 
convex  lens.  Where  it  joins  the  white  portion  of  the  sclerotic  it  forms 
a  circular  outline.  The  motor  muscles  are  attached  to  the  sclerotic. 
The    cornea  is    made  up  of  four  layers,  the  outer  of  which  is  the  con- 


OCULAR         REFRACTION 


A  (liagramniitic  representation 
S. — The  sclerotic. 
R. — Tlie  retina. 
A. — The  aqueous  humor. 
V. — The  vitreous  humor. 
O. — The  optic  nerve. 
I. — The  iris. 
X. — The  centre  of  rotation  of  the  eye. 

The  straight  line  through  the  centre  of  lotation  lo  the  yellow  spot 
vision. 

The  clotted  circle  shows  the  relative  departure  ftoni  spherical  form 
normal  eye 


e  9t. 

tical  cross  section  of  the  humai 

Ch.— The  choroid 

C. — The  cornea. 

L.— The  crystalline  lens. 

Y. — The  yellow  spot,  or  niacu 

P. — The  pupil. 

M.— The  ciliary  muscle. 


indi 


le   of 
ately 


The  crystalline  lens  is  shown 
The 


havi 
given  in  this  cut  are  not 
cipal  parts  of  the  eye. 


nucle 


and  surrounding  layers. 
J  to  be  exact,  it  is  merely 


1'  II  V  S   I  O  L  O  G  V         AND         A   X  A   T  O  M   V.  103 

junctiva.  The  portion  of  the  conjunctiva  covering  the  cornea  is  very 
thin  and  is  free  from  vessels,  it  is  the  mucous  membrane  of  the  eye 
and  covers  the  whole  of  the  outer  surface,  also  extending  continuously 
and  forming  the  inner  coating  of  the  eyelids. 

The  sclerotic  is  pierced  at  its  inner  or  posterior  portion  by  the 
optic  nerve  as  it  enters  the  globe  of  the  eye. 

The  middle  or  second  membrane  is  the  choroid,  it  terminates  for- 
ward in  the  ciliary  processes  and  the  iris.  The  iris  is  the  curtain  to 
regulate  the  amount  of  light  entering  the  eye  and  assumes  various 
colors  in  different  individuals,  it  is  that  which  makes  a  blue  or  a  brown 
eye,  etc.  The  iris  is  pierced  by  a  circular  opening  called  the/?////, 
it  is  merely  a  round  hole  in  the  curtain;  it  contracts  and  expands  as 
the  light  increases  or  decreases  in  intensity,  the  expansion  and  con- 
traction being  a  purely  involuntary  action. 

The  ciliary  muscle,  which  is  the  termination  of  the  ciliary  proces- 
ses, is  behind  the  iris  and  surrounds  the  crystalline  lens;  by  its  action, 
contracting  around  the  periphery  of  the  lens,  it  permits  the  increase 
of  the  convexity  of  the  crystalline  lens  and  therefore  its  refracting 
power.  This  action  constitutes  the  power  of  the  eye  to  accommodate 
its  refraction  to  focus  light  rays  from  objects  at  any  distance. 

The  color  of  the  choroid  is  a  deep  brown  to  black.  It  is  pierced 
at  the  back  of  the  eye  by  the  optic  nerve  the  same  as  the  sclerotic. 
The  choroid  is  made  up  largely  of  the  blood  vessels  of  the  eye  and  the 
pigment  that  absorbs  the  light 

The  inner  membrane  is  the  retina.  It  is  the  expansion  of  the 
optic  nerve  after  it  enters  the  globe  of  the  eye  and  is  the  nervous  sys- 
tem that  is  sensitive  to  light.  The  retina  decreases  in  thickness  as 
it  spreads  toward  the  front  of  the  globe  and  also  decreases  in  sensi- 
tiveness to  light. 

The  optic  nerve  shows  with  the  ophthalmoscope  as  a  round  white 
disk,  the  point  where  the  nerve  enters  the  eye  is  not  sensitive  to  light 
and  forms  the  "  blind  spot  "  of  the  eye.  Toward  the  outer  side  of  the 
disk  is  the  ''yello:.'  spot,"  or  the  viacnla  hit  en,  which  is  a  slight 
depression  in  the  retina,  at  which  the  greatest  sensitiveness  exists, 
and  upon  which  the  line  of  vision  falls  when  we  look  at  an  object; 
thuSj  we  are  compelled  to  change  ihe  direction  of  the  look  as  we  view 
different  objects.  The  retina  decreases  in  sensitiveness  to  light  and 
sight  impressions  in  every  direction  from  the  yellow  spot  in  concen- 
tric circles. 

The  optic  nerves  originate  in  each  half  of  the  brain;  they  unite 
then  separate,  having  crossed  each  other,  and  each  passes  through  the 


104  OCULAR  R   K   F  R  A  C  T   I   O  N. 

opiic  foramen,  or  aperture  in  the  sphenoid  bone,  leading  into  the  orbital 
cavity  of  its  respective  eye. 

The  central  artery  enters  the  eye  with  the  optic  nerve,  and,  with 
its  branches,  may  be  plainly  seen  with  the  ophthalmoscope  as  they 
spread  out  over  the  retina. 

The  aqueous  or  watery  humor,  fills  the  space  between  the  crystal- 
line lens  and  the  cornea,  and  serves  to  distend  the  cornea  and  give  to 
it  its  form.  The  vitreous  humor^  a  jelly  like  substance,  fills  the  space 
between  the  crystalline  lens  and  the  retina  and  distends  the  globe  of 
the  eye,  forming  its  largest  bulk. 

The  crystalline  humor  or  lens  is  in  form  similar  to  a  double  con- 
vex lens,  the  outer  surface  is  less  convex  than  the  inner  surface.  It 
is  situated  immediately  behind  the  iris  and  is  contained  in  a  trans- 
parent, elastic  membrane  called  the  capsule  of  the  lens.  It  is  com- 
posed of  concentric  layers,  the  outer  of  which  are  soft  and  elastic  but 
they  increase  in  density  and  toughness  toward  the  centre  The  lens 
measures  about  ten  millimeters  in  diameter  and  about  four  millimeters 
in  thickness.  It  is  perfectly  transparent  and  without  color,  this  is  also 
the  condition  of  the  other  humors  when  the  eye  is  in  a  normal  healthy 
condition. 

Tscherning  gives  an  interesting  description  of  the  crystalline  lens, 
among  other  facts  he  states  that:  "It  must  be  noticed  in  the  first 
place  that  this  body  is  not  homogeneous;  its  index  gradually  dimin- 
ishes starting  from  the  centre  of  the  nucleus  towards  the  periphery. 
The  curvature  of  its  layers  diminishes  also  towards  the  periphery,  so 
that  each  layer  takes  the  form  of  a  meniscus,  the  concavity  of  whii.h 
is  greater  than  the  convexity." 

Movement  is  imparted  lo  the  eyes,  in  order  that  the  line  of  vision 
may  be  changed,  by  six  muscles  to  each;  by  the  action  of  these  mus- 
cles opposing  each  other,  the  eyes  are  rotated  about  various  axes  of 
rotation  and  one  centre  of  rotation. 

T/ie  motor  muscles  of  the  eye  are  the  Superior,  Inferior,  Internal, 
External  and  tlie  Superior  and  Inferior  Oblique  muscles. 

The  four  mentioned  first  are  the  principal  ones,  and  as  their 
names  indicate,  they  are  attached  to  the  eye  forward  of  its  center 
respectively  upon  the  upper,  lower,  inner  and  outer  portion  of  the 
sclerotic.  These  four  muscles  are  in  the  form  of  straight  flat  bands 
that  spread  out  and  attach  themselves  to  the  eye  in  a  fan  like  forma- 
tion at  their  termination.  The  internal  recti  turn  the  eyes  inward, 
creating  convergence  of  the  visual  lines.  The  internal  is  the  largest 
of  the  muscles  and  is  attached  the  farthest  forward  of  all,  reaching 
almost  to  the  edge  of  the  cornea. 


H   V  S   I  ()  I.  ()  C,  V         A   N    l>         A  N  A  T  O   M   V. 


105 


The  external  rceti  are  attached  opposite  the  internal  and  rotate 
the  eyes  outward.  The  superior  recti  turn  the  eyes  upward  and  the 
inferior  rrr/?' downward. 

The  superior  oblique  rectus  is  not  straight  but  passes  over  a  kind 
of  roll,  which  acts  as  a  pulley,  and  is  attached  to  the  posterior  of  the 
globe,  it  rotates  the  eye  inward  and  upward. 

The  inferior  oblique  rectus  turns  the  eye  inward  and  down. 

It  will  be  noted  that  only  one  muscle  tends  to  turn  the  eye  out- 
ward, all  the  others  combine  to  rotate  it  inward. 

In  a  concise  description  of  the  eye  by  Ludovic  Hirschfeld,  he 
says: — "The  sclerotic  is  a  tunic  of  protection,  and  the  cornea  a 
medium  for  the  transmission  of  light.  The  choroid  supports  the  ves- 
sels destined  for  the  nutrition  of  the  eye,  and  by  its  pigmentum  nig- 
rum absorbs  all  loose  and  scattered  rays  that  might  confuse  t  e  image 
impressed  upon  the  retina.  The  iris  by  means  of  its  powers  of  e.\- 
pansion  and  contraction,  regulates  the  quantity  of  light  admitted 
through  the  pupil.  If  the  iris  be  thin,  and  the  rays  of  light  pass 
through  its  substance,  they  are  immediately  absorbed  by  the  uvea, 
and  if  that  layer  be  insufficient,  they  are  taken  up  by  the  black  pig-- 
ment  of  the  ciliary  processes. 

"  In  Albinos,  where  there  is  an  absence  of  pigmentum  nigrum, 
the  rays  of  light  traverse  the  iris,  and  even  the  sclerotic,  and  so  over- 
whelm the  eye  with  light,  that  sight  is  destroyed,  except  in  the  dim- 
ness of  evening,  or  at  night. 

"In  the  manufacture  of  optical  instruments,  care  is  taken  to  color 
their  interior  black,  with  the  same  object,  the  absorption  of  scattered 
rays.  The  transparent  lamellated  cornea,  and  the  humors  of  the  eye 
have  for  their  office  the  refraction  of  the  rays  in  such  proportion  as  to 
direct  the  image  in  the  most  favorable  manner  upon  the  retina." 

For  a  description  of  the  nerves  of  motion  and  feeling  of  the  eye 
the  student  may  consult  any  standard  work  on  anatomy  of  the  human 
body. 


CHAPTER  V. 
PHYSIOLOGICAL  OPTICS. 


AS  the  title  of  this  chapter  indicates,  it  treats  of  the  forination  of 
images  by  the  human  eye.  The  method,  by  which  this  is  ac- 
complished, is  based  upon  the  principles  of  refraction  with  which 
the  student  is  now  familiar.  The  eye,  as  an  optical  instrument,  is 
frequently  compared  to  a  camera,  and,  no  better  comparison  could 
possibly  be  made.  To  make  good  photographs  the  refracting  system 
must  be  perfect  and  the  screen,  or  plate,  must  be  "in  focus."  In  order 
that  perfect  vision  may  be  had,  the  refraccing  system  of  the  eye  must 
be  free  from  errors  and  the  retina  must  be  situated  at  the  focal  point 
of  the  system. 


Figure  ',2. 

Seclional   view   ot  a  camera,  llie  parallel  lines  represent  liglit  rays  entering   the   lens   and 
brought  to  a  focus  on  ll.e  plate. 

In  figure  92  is  shown  a  sectional  view  of  a  camera,  the  lens  tube, 
projecting  from  the  body  of  the  camera,  carries  the  refracting  system. 
The  parallel  lines  represent  light  rays  from  an  object  more  than 
twenty  feet  distant,  they  enter  the  lens  aperture  and  undergo  refrac- 
tion by  the  achromatic  lens;  just  behind  the  lens  is  situated  the  dia- 
phragm, which  cuts  out  the  marginal  rays  and  corrects  the  spherical 
aberration.  Beyond  the  diaphragm,  the  rays  are  seen  converging  to  a 
point  upon  the  sensitive  plate  at  the  back  of  the  camera.  The  bellows 
arrangement  for  focussing  the  camera,  by  changing  the  position  of 
the  plate  with  regard  to  the  lens,  is  not  shown  in  the  diagram,  every- 


PHYSIOLOGICAL  OPTICS.  107 

one  knows  how  a  camera  is  made  and   it   was  not   thought   necessary 
to  show  this. 

The  parallel  rays  shown  in  the  figure  are  supposed  to  come  from 
a  single  point  upon  the  object,  their  focus  thus  represents  but  a  single 
point  in  the  image.  The  image  of  the  object  is  made  up  of  innumera- 
ble focal  points,  in  fact,  in  order  to  be  a  perfect  image,  it  must  consist 
of  the  focus  of  rays  of  light  from  every  point  of  the  object. 


Sectional  view  of  the  eye  showing  Ihe  similarity  to  the  action  of  a  camera;   parallel  rays  o 
light  being  brought  to  a  focus  upon  the  retina. 

Figure  93  is  a  sectional  view  of  the  eye,  for  comparison  with  the 
camera  under  similiar  conditions,  as  shown  in  figure  92. 

The  parallel  rays  enter  the  aperture  of  the  eye  which  is  the  cor- 
neal surface,  undergo  refraction  by  the  cornea,  a  portion  are  dia- 
phragmed  out  by  the  iris,  the  remainder  undergo  more  refraction  by 
the  crystalline  lens  and  focus  upon  the  retina  without  any  effort  of 
the  accommodation. 

The  ideal  conditions  of  vision  are  only  obtained  with  a  normal  or 
emmetropic  eye,  the  conditions  that  exist  in  such  an  eye  will  first  be 
explained.      Figure  93  represents  an  emmetropic  eye. 

The  refracting  system  of  the  eye  is  made  up  of  the  cornea,  cry- 
stalline lens  and  the  humors,  its  aberrations  are  partially  corrected  by 
the  iris,  acting  as  a  diaphragm  and  the  difference  in  the  index  of  re- 
fraction and  the  power  of  dispersion  of  the  various  parts. 

The  index  of  refraction  of  the  cornea  is  1.37  ;  of  the  crystalline 
lens  1.42;  of  the  aqueous  and  vitreous  humors  1.33;  comparison  being 
made  with  air  as  a  standard,  the  index  of  refraction  of  air  being  taken 


as  i.oo.       The   eye  is  not  achromatic,  but  the  pupil,  by  contracting, 
reduces  the  chromatic  aberration  as  well  as  the  spherical  aberration. 

The  refracting  system  of  the  emmetropic  eye  is  about  (58. D.) 
fifty  eight  dioptres  in  power,  this  means  that  the  focal  length  of  the 
eye  is  about  (.7)  seven- tenths  of  an  inch.  Of  the  dioptric  power  of 
the  eye,  the  cornea  contributes  about  (42.5  D.)  forty  two  and  a  half 
dioptres,  the  crystalline  lens  about  (15.5  D.)  fifteen  and  a  half  dioptres. 
To  comprehend  what  this  means,  and  realize  how  powerful  and  sensi- 
tive an  instrument  of  refraction  the  eye  is,  if  one  will  consider  that  in 
the  test  case  the  most  powerful  convex  spherical  lens  is  a  20. D., and  if 
the  eye  had  a  dioptric  power  of  this  amount,  it  would  have  to  be  two 
inches  in  diameter,  some  idea  will  be  obtained.  If  the  eye  were  only 
an  inch  in  diameter  it  would  require  40  D.  of  refraction;  but  as  it 
possesses  nearly  60.  D.  it  is  only  a  little  more  than  three  quarters  of 
an  inch  in  its  antero  posterior  diameter. 

The  refracting  system  of  an  emmetropic  eye  is  in  effect  a  convex 
spherical  lens;  having  equal  refraction  in  every  meridian,  the  curva- 
ture of  the  cornea  must  be  the  same  in  every  meridian.  This  is  also 
true  of  the  surfaces  of  the  crystalline  lens. 

When  designating  the  dioptric  power  of  a  lens  as  a  4.00  D.  it  is 
understood  to  mean  that  it  possesses  the  power  to  bring  pa)-alle/  rays 
of  light  to  a  focus  at  a  distance  of  10  inches,  or  that  its  principal  focus 
is  four  dioptres. 

When  the  statement  is  made  that  an  emmetropic  eye  has  58.  D. 
of  refraction,  it  means  that  parallel  rays  of  light  entering  such  an  eye 
are  brought  to  a  focus  exactly  upon  the  retina,  which  is  situated  at 
e   actly  the  focal  point  of  the  system. 

The  image  created  upon  the  retina  is  ?-i-al  and  inverted;  that  we 
do  not  see  things  up  side-down  is  difificult  to  explain,  just  as  it  is  im- 
possible to  tell  exactly  where  the  seat  of  sight  is  located  in  the  brain, 
and/^ow  zvc  sec.  It  is  evidently  a  matter  of  education,  one  of  the  things 
we  learn  intuitively  without  knowing  or  realizing  how  we  learn  it. 

It  has  never  been  determined  accurately  what  is  the  standard  of 
a  normal  eye,  that  is,  just  how  much  dioptric  power  it  should  possess. 
The  reason  for  this  is  obvious  There  is  no  doubt  that  there  exists  a 
difference  in  the  axial  length  of  the  eyes,  yet  if  the  dioptric  power  of 
each  is  such  that  the  retina  is  situated  at  exactly  the  principal  focus 
of  the  system,  normal  sight  conditions  will  obtain.  Thus  different 
eyes  may  be  emmetropic,  yet  they  may  have  different  powers  of  re- 
fraction. It  is  quite  possible  to  select  a  number  of  men  and  class 
e.ich  as  perfect  specimens  of  manhood;  though  there  may  exist  a  wide 


comparative   difference  between   them,  yet  so  long  as  each  possesses 
the  required  proportions,  each  may  be  perfect. 

A  definition  of  a  normal  eye  may  be  given  as: — 

An  emmetropic  eye  is  one  possessing  equal  refraetion  in  every  meri- 
dian, the  retina  is  situated  exaetly  at  the  principal  foeiis  of  its  refraet 
ing  system  under  static  conditions  {/!r  static  eondilions  a  state  of  rest 
is  meant  ) 

It  will  be  remembered  that  light  rays  coming  from  a  distance  of 
twenty  or  more  feet  are  in  effect  parallel.  If  any  object  situated  at  this 
distance  be  viewed, the  rays  from  it  enter  the  emmetropic  eye  and  pass 
ing  through  the  refracting  system  are  brought  to  a  focus  upon  the 
retina,  without  any  effort,  forming  a  real  image  thereon.  This  optical 
condition,  due  to  light  impulse,  creates  a  nerve  impulse  in  the  retina, 
which  is  transmitted  through  the  optic  nerve  to  the  centers  of  vision 
in  the  brain;  there,  some  mysterious  action  takes  place  and  sight  is 
the  result. 

Suppose  the  object  seen  be  approached,  so  that  it  is  much  nearer 
to  the  eye  than  twenty  feet,  the  light  rays  will  no  longer  be  parallel 
when  they  enter  the  eye  but  will  be  divergent,  the  degree  of  diver- 
gence increasing  the  nearer  the  object  is  approached.  Now,  if  as 
parallel  rays  they  focussed  upon  the  retina,  as  divergent  rays  they  will 
not,  but  would  come  to  a  focus  at  a  point  back  of  the  retina.  In  order 
to  overcome  this  condition  the  antero-posterior  diameter  of  the  eye 
would  have  to  lengthen,  thus  carrying  the  retina  farther  away  from 
the  refracting  system,  or  the  refraction  of  the  eye  would  have  to  be 
increased  to  enable  it  to  adapt  itself  to  the  divergent  rays. 

The  latter  is  what  actually  takes  place,  Ihe  refracting  system 
changes  its  power,  accommodating  it  to  focus  either  parallel  or  diver- 
gent rays  upon  the  retina.  This  is  called  the  accommodation  of  the  eye. 

Accommodation  is  accomplished  by  an  increase  in  the  convexity  of 
the  anterior  surface  of  tlie  crystalline  lens,  the  ciliary  muscle  by  con. 
tracting  permits  the  lens  to  bulge  forward  of  its  own  inherent  elasticity _ 

Let  figure  94  represent  a  sectional  view  of  the  crystalline  lens. 
The  anterior  surface  has  a  longer  radius  than  the  posterior,  and  there- 
fore has  less  refracting  power,  in  fact,  in  a  state  of  rest,  the  anterior 
surface  has  only  about  two-thirds  of  the  refracdng  power  of  the  pos 
terior.  The  refracting  power  of  the  anterior  surface  is  about  +  6.  D., 
of  the  posterior  surface  about  -f  9  50  D.,  when  the  crystalline  lens 
possesses  its  minimum  refracting  power. 

When  the  accommodation  is  exerted  the  curvature  of  the  anterior 
surface  increases,  that  is,  it  deepens,  and    its   radius   becomes   much 


O  C  U   L  A 


R   A  C  T   I  O   X. 


smaller.  This  increases  the  refracting  power  of  this  surface  and 
therefore  adds  to  the  refracting  power  of  the  lens. 

The  dotted  line  indicates  the  curvature  of  the  anterior  surface 
under  accommodation.  The  position  of  the  iris  and  pupil  are  shown 
during  accommodation. 

This  diagram  is  purposely  made  large  and  the  curvatures  shown 
are  exaggerated,  so  that  it  may  readily  be  seen  what  takes  place  to 
effect  accommodation,  or  change  of  focus  in  the  eye.  A,  indicates  the 
anterior  surface ;  P,  indicates  the  pupil. 


Sectional    view  of  the   crystalline  lens  in  a  static  condition,  also  with  the  accommodation 

e-terted.     The  dotted  line  indicates  the  change  in  the  curvature  of  the  anterior  surface  during 

accommodation.     The  position  of  the  iris  and  contraction  of  the  pupil  is  also  indicated  during 

accommodation.     A,  indicates  the  anterior  surface;   P,  the  pupil. 

When  an  eye  is  in  a  static  condition,  or   state  of  rest;  it  possesses 
its  least  refraction  and  is  therefore  focussed  for  the  greatest  distance 


PHYSIOLOGICAL         OPTICS.  i ,  i 

possible  for  it.  Under  these  conditions  it  is  said  to  be  focussed 
ior  \X.s  far  point,  or  punctiini  rcviotniii. 

When  the  accommodation  is  exerted  to  its  fullest  power,  the  eye 
possesses  its  greatest  refraction.  It  is  then  focussed  for  its  near  point, 
or punctuiii  proxiuium. 

Objects  situated  at  the  near  point  of  an  eye  may  be  seen  distinct- 
ly because  the  eye  will  focus  the  divergent  rays  and  create  a  clear 
image,  if  the  object  be  brought  closer  than  the  near  point,  a  clear 
image  cannot  be  formed,  and  distinct  vision  cannot  be  had. 

The  distance  between  the  near  and  the  far  point  is  called  the 
range  of  accoiiiuiodation  of  the  eye. 


Figure  95. 

Diagram  to  represent  an  emmetro|)ic  eye   adapted  for   distant  vision.      Parallel  rays  of  liglit 
are  brought  to  a  focus  upon   the   retina.      Tlie  pupil  is  expanded,  or  rather,   not  contracted. 

The  amount  to  which  an  eye  is  capable  of  increasing  its  refraction 
is  called  its  amplitude  of  accommodation,  it  is  measured  in  dioptres. 

The  amplitude  of  accommodation  decreases  with  age,  at  about 
the  age  of  ten  years  it  begins  to  be  manifest.  With  the  decrease  in 
the  amplitude,  the  range  of  accommodation  necessarily  becomes  less 
and  less,  and  in  order  to  see  clearly,  a  person  must  hold  print  farther 
and  farther  away.  When  a  person  is  unable  to  read  average  news- 
paper and  book  print  at  ten  inches,  because  of  the  decrease  in  the 
amplitude  of  accommodation,  presbyopia  is  said  to  have  commenced. 
Presbyopia  will  be  explained  later. 

It  is  obvious  that  the  amount  of  accommodation  required  will 
depend  upon  the  distance  the  object  it  is  desired  to  see  is  situated  from 
the  eye.  From  a  distance  of  forty  inches,  the  divergent  rays  would 
be  rendered  parallel  by  a  one  dioptre  convex  s])here,  therefore,  the 
eye  would  have  to  accommodate  one  dioptre.       If  the  object  be  ten 


112  OCULAR         REFRACTION 

inches  away,  four  dioptres  will  have  to  be  supplied  by  the  accommo- 
dation. It  will  thus  be  noted  that  all  of  the  accommodation  is  not 
necessarily  used  at  all  times.  All  the  accommodation  is  required  to 
see  an  object  situated  at  the  near  point  of  the  eye. 

Accommodation  is  an  involuntary  action,  the  same  as  the  contrac- 
tion and  expansion  of  the  pupil  is  involuntary,  and  for  this  reason  few 
people  are  conscious  of  the  act. 

Let  figure  95  represent  an  emmetropic  eye  adapted  for  distant 
vision.  The  pupil  is  shown  expanded  and  parallel  rays  entering  are 
brought  to  a  focus  upon  the  retina. 

Figure  96  represents  this  same  eye  adapted  to  bring  to  a  focus 
upon  the  retina  the  rays  from  the  object  at  P  which  is  ten  inches 
away.  The  accommodation  exerted  is  four  dioptres.  The  lens  is 
shown  having  a  deeper  curvature  upon  its  anlerior  surface.      The  pu. 


Figure  96. 

Diagram  to  represent  nn  emmetropic  eye  adapted  tor  vision  at  close  point.        Di\cii;ent  r.iys 
ot  light  are  brought  to  a  focus  upon  the  retina.      The  pupil  is  contracted. 

pil  is  also  contracted,  an  action  that  occurs  with  accotnmodation. 

A  simple  experiment  to  detect  the  act  of  accommodation  in  one's 
own  eye  inay  be  made  by  anyone.  Stand  before  a  window  having  a 
lace  curtain  before  it,  let  the  eyes  be  eight  or  ten  inches  from  the 
curtain.  Look  across  the  street  and  the  mesh  of  the  lace  will  disap- 
pear. Without  any  movement  of  the  head  now  look  at  the  threads  of 
the  curtain;  when  they  appear  distinctly,  the  object  across  the  street 
will  have  becotne  so  blurred  as  to  be  indistinguishable. 

Why  is  it  that  the  distant  object  disappeared  when  looking  at  the 
curtain,  and  the  mesh  of  the  curtain  disapipeared  when  looking  at  a 
distance  ?  The  rays  of  light  from  both  objects  enter  the  eyes  all  the 
time. 


Let  figure  97  represent  the  emmetropic  eye  adjusted  for  distance, 
the  parallel  rays  focus  upon  the  retina.  The  divergent  rays  from  the 
point  P,  represented  by  the  dotted  lines,  do  not  focus  upon  the  retina 


An   emmetropic  eye  adapted  for  distance,   the  divergent  rays  represented  by  dotted  lines, 
form  circles  of  diffusion  upon  the  retina    their  focus  being  behind  the  retina. 

but  at  the  point  P'  back  of  it.  The  rays  from  the  object  at  P  form 
circles  of  diffusion  upon  the  retina  and  the  object  does  not  appear 
distinctly. 


Figure 

An  emmetropic  eye  adapted  for  a  near  point.     The  parallel  rays,  represented  by  dotted  lines 
form  circles  of  diffusion  upon  the  retina,  their  focus  being  in  front  of  the  retina. 

Figure  98  represents  the  eye  adjusted  for  the  object  P.  Parallel 
rays  from  distant  objects  enter  the  eye  at  the  same  time  but  are 
brought  to  a  focus  at  F,  a  point  in  front  of  the  retina.  The  dotted 
lines   represent  rays    from  the  distant  object,  they  meet  and  cross  at 


114  OCULAR         U   E   F  R  A  C  T   1   O  X. 

the  point  F,  then  diverge  and  reach  the  retina  lo  form  circles  of    iffu- 
sioD,  and  therefore  no  distinct  image. 

//  is  thus  demonstrated,  that  the  eye  sees  clearly,  only  those  objects 
lying  in  the  /'lane  for  ivhick  it  is  at  the  instant  adj'ttsted. 

In  looking  about  a  room  of  average  size,  in  looking  at  objects 
within  one's  reach,  in  reading,  etc.,  it  is  seen  that  the  accommodation 
must  be  constantly  in  action.  The  more  we  know  of  this  wonderful 
function  of  the  eye,  the  more  marvelous  we  find  it  to  be.  Our  visual 
comfort  is  largely  dependent  upon  the  action  of  the  accommodation. 
If  excessive  demands  are  made  upon  it  for  any  cause,  we  suffer  for  it 
in  visual  discomfort. 

There  seems  to  be  so  much  uncertainty  in  the  minds  of  many 
about  the  theory, and  the  mechanism  of  the  accommodation,  and  it  has 
such  an  important  bearing  upon  the  work  of  the  refractionist,  that  the 
student  is  urged  to  study  the  subject  carefully.  The  limits  of  this 
work  preclude  the  possibility  of  covering  the  subject  fully,  nor  is  it 
necessary,  in  view  of  the  excellent  works  in  existence.  Tscherning's 
Physiologic  Optics  is  recommended,  the  chapter  on  accommodation  is 
particularly  valuable. 

A  few  extracts  will  be  quoted  from  it.  "  To  explain  the  mechan- 
ism of  accommodation  Helniholtz  announced  the  following  hypothesis, 
which  he  gave,  however,  only  as  probable:  In  a  state  of  repose  the 
crystalline  lens  is  kept  flattened  by  a  traction  exerted  by  the  zonula. 
When  the  ciliary  muscle,  of  which  he  considered  the  anterior  extrem- 
ity as  fixed,  contracts,  it  draws  the  choroid  slightly  forward,  which 
relaxes  the  zonula.  Having  become  free,  the  crystalline  lens  then 
swells  by  its  own  elasticity,  approaching  the  spherical  form." 

"  This  hypothesis  does  not  seem  to  have  been  at  first  generally  ac- 
cepted. Hencke  and  other  authors,  tried  to  explain  the  phenomena  ob- 
served, by  other  hypotheses.  After  having  discovered  the  supposed 
circular  fibres  of  the  ciliary  muscle,  H.  Mitller  thought  that  this  muscle 
changed  the  form  of  the  crystalline  lens  by  a  direct  pressure,  an  idea 
which  was  abandoned  when  it  became  known  that  the  ciliary  body 
never  touches  the  crystalline  lens.  ' 

"The  contents  of  the  crystalline  lens  are  composed,  in  the  adult 
of  two  parts,  the  nucleus,  which  cannot  change  its  form,  and  the  sup- 
erficial layer,  which,  on  the  contrary,  possesses  this  faculty  to  a  very 
high  degree;  its  consistence  is  very  nearly  that  of  a  solution  of  very 
thick  gum.  I  call  this  layer  the  aeeoinmodative  layer  in  order  to  show 
that  it  is  due  to  it  that  the  eye  can  accommodate  itself.  Accordingly 
as  age  advances,  the  nucleus  increases  while  the  accommodative  layer 


PHYSIOLOGICAL  OPTICS.  115 

diminishes, and  with  it  the  amplitude  of  accommodation.  The  whole 
is  surrounded  by  a  capsule  which  is  inextensible  or  very  nearly  so." 

"  It  has  always  been  supposed  that  a  traction  exerted  on  the 
zonula  must  flatten  the  crystalline  surfaces,  while  a  pressure  exerted 
on  the  borders  would  have,  on  the  contrary,  the  effect  of  increasing 
their  curvature.  Nothing  of  the  kind :  a  pressure  exerted  on  the 
borders  has,  on  the  contrary,  the  effect  of  flattening  the  surfaces, 
while  a  traction  exerted  on  the  zonula  increases  the  curvature  of  the 
surfaces  at  the  middle,  while  flattening  them  toward  the  periphery." 

"  To  verify  this  fact  we  take  tr.e  crystalline  lens  from  the  eye  of 
an  ox  or  a  horse,  which  must  not  be  too  old,  with  the  capsule  and 


Figure  99. 

Change  of  form  the  crystalline  lens  assumes:  A,  when  pressure  is  e.xerted  upon  the  periphery; 

B.    when  a  pull   is   exerted   upon   the   zonula.       (This   cut   reproduced    from    Tscherning's 

Physiologic  Optics.) 

zonula  of  Zinn.  It  is  easy  to  see  that  by  compressing  the  borders  the 
surfaces  are  flattened;  to  observe  the  effect  of  traction  we  take  hold 
of  the  zonula  on  both  sides,  very  near  the  crystalline  lens,  and,  by 
pulling,  we  can,  on  looking  at  the  crystalline  lens  sideways,  see  that 
the  anterior  surface  assumes  a  hyperbolic  form." 

See  figure  99.  The  dotted  line  indicates  the  form  which  the 
crystalline  lens  assumes:  A,  by  a  lateral  pressure;  B,  by  a  traction 
exerted  upon  the  zonula.  The  arrows  indicate  the  direction  of  the 
forces. 


no  OCULAR  R  E  F   R   A  C  T   I  O  N. 

The  conditions  governing  refraction  in  the  normal  eye  being 
understood,  we  will  turn  once  more  to  the  analogy  of  the  camera  to 
explain  another  condition  required  to  obtain  vision. 

In  making  a  photographic  picture  of  some  object,  the  camera  is 
directed  toward  the  object,  so  that  its  image  occupies  a  prominent 
position  on  the  plate.  The  plate  being  then  focussed  for  the  object, 
some  of  the  other  objects  in  the  picture  will  no  doubt  be  out  of  focus. 

In  order  that  the  eye  may  register  the  image,  it  is  not  merely 
necessary  that  the  image  be  focussed  upon  the  retina  by  the  refract- 
ing systern,  but  it  must  fall  upon  a  certain  portion  of  the  retina. 

There  is  a  point  in  the  retina  that  is  more  sensitive  than  any 
other  to  light  impressions,  it  is  called  the  iiiacii/a  liitca,  and  in  order 
that  the  clearest  perception  ot  an  object  may  be  had,  its  image  must 
fall  upon  the  macula. 

In  order  that  this  may  occur,  the  eye  is  said  to  ''fix  "  the  object 
it  is  desired  to  see.  A  straight  line  drawn  from  the  object  fixed, 
through  the  optical  centre  of  the  refracting  system  to  the  macula,  is 
the  //«(■  of  i'isio>i.  This  explains  the  shifting  movements  of  the  eyes 
in  their  orbits,  the  line  of  vision  being  changed  from  point  to  point  of 
fixation.  As  the  image  falls  upon  a  portion  of  the  retina  removed 
from  the  region  of  the  macula  it  is  indistinct;  the  farther  away  from 
the  macula,  the  less  distinctly  the  eyes  can  discern  objects,  until  the 
limit  of  visual  impressions  of  the  retina  is  reached. 

When  fixing  an  object,  the  eye  also  perceives  other  objects  sur- 
rounding it,  less  distinctly  the  farther  they  are  removed  to  the  right 
or  left,  above  or  below  it. 

The  amount  of  space  the  eye  perceives  at  one  time,  when  fixed 
upon  an  object,  is  called  ihe  Jiehi  of  vision. 

The  macula  lutea  is  the  centre  of  vision  in  the  visual  field,  whi:h 
is  in  the  form  of  an  irregular  oval,  but  the  macula  is  not  in  the  centre 
of  the  field. 

The  line  of  vision  corresponds  nearly  to  the  principal  axis  of  the 
eye. 

In  the  last  paragraph  of  Chapter  III.  reference  is  made  to  binocu- 
lar vision  ;  it  means,  si7iglc  vision  with  two  eyes.  Each  eyes  receives 
its  own  image  and  records  it,  the  two  are  transmitted  to  the  brain 
and  there  fused  into  one. 

So  tar,  only  single  vision  has  been  considered,  but  in  the  work  of 
ocular  refraction,  this  condition — binocular  vision — must  be  taken  in- 
to account,  for  it  involves  the  most  complications  that  occur  in  the 
correction  of  errors  of  refraction. 


Let  us  see  how  binocular  vision  is  brought  about. 

Take,  for  example,  a  person  having  a  pair  of  eyes  that  are  em- 
metropic. Suppose  him  to  observe  an  object,  looking  at  it  with  both 
eyes  If  one  be  covered,  he  will  see  the  object  with  the  other,  show- 
ing that  single  vision  exists.  Now  repeat  the  experiment,  covering 
the  other  eye  ;  again,  single  vision  obtains.  This  proves  that  vision 
is  recorded  with  each  eye. 

With  both  eyes  directed  toward  the  object,  only  single  vision 
occurs,  showing  that  in  some  mysterious  manner,  or  rather  by  some 
mental  process,  the  two  retinal  images  are  blended  or  fused  into  one. 

It  has  just  been  demonstrated,  that  the  eye  must  "  fix  "  an  object 
to  see  it  clearly.  When  binocular  vision  is  had,  each  eye  separate- 
ly must  "  fix  "  it.  This  requires,  as  we  have  seen,  a  muscular  action; 
the  recti  being  called  into  play. 

This  involves  intimate  relations  of  the  li'nes  of  vision  of  the  two 
associated  eyes,  so  that  like /portions  of  each  image  falls  upon  identical 
points  in  the  retina  of  each  eve. 

When  normal  conditions  of  the  rtiotor  muscles  of  the  eyes  exist, 
binocular  vision  is  made  possible  by  a  co-ordination  of  the  lines  of 
vision.  This  is  called  Orthophoria,  any  deviation  from  it  is  called 
Heteroplioria. 

Binocular  vision  exists  as  a  result  of  the  combined  action  of  Re- 
fraction, Accommodation  and  Co  ordination  of  the  lines  of  vision. 

An  emmetropic  eye,  observing  an  object  at  a  distance  of  twenty 
or  more  feet,  exercises  no  accommodation,  because  the  rays  of  light 
that  reach  the  eye  from  the  object  are  parallel. 

When  two  emmetropic  eyes  are  associated,  in  looking  at  a  distant 
object,  they  do  not  accommodate,  and  it  is  also  considered  that  their 
visual  lines  are  parallel. 

If  an  object  nearer  than  twenty  feet  is  observed,  the  visual  lines 
are  no  longer  considered  to  be  parallel,  but  they  converge  to  meet  at 
the  point  observed. 

This  is  called  the  Convergence  of  the  eye. 

It  is  known  that  undsr  these  conditions  accommodation  is  also 
required,  to  focus  the  light  rays  from  the  object  upon  the  retina. 

Accommodation  and  Convergence  are  intimately  related. 
Nature  intended  that  they  should  be  so  associated,  that  they  should 
work  together  in  harmony.  Wnen  we  accommodate,  we  should  also 
converge  ;  when  we  converge,  we  should  also  accommodate, 

A  given  amount  of  accommodation  should  be  accompanied  by  a 
definite  degree  of  convergence. 


us  OCULAR         R  E   K   R  A  C  T   I  O  X. 

The  degree  of  convergence  is  measured  by  what  is  termed  a 
meter-angle;  it  corresponds  to  the  unit  of  refraction,  the  dioptre. 
The  meter-angle  is  not  a  fixed  quantity  like  the  dioptre,  because  it 
varies  in  different  persons  according  to  the    inter- pupillary    distance. 

Any  departure  from  normal  conditions  of  refraction  disturbs  the 
harmonious  action  of  accommodation  and  convergence.  Such  dis- 
turbance i-s  frequently  the  cause  of  ocular  distress. 


The  optical  functions  of  the  human  eye  have  so  far  been  ex- 
plained, and  comparisons  have  been  drawn  between  it  and  an  optical 
instrument.  In  so  doing,  only  normal  conditions  of  refraction  in  the 
eye  have  been  discussed,  to  show  how  the  eye  is  capable  of  creating 
images,  and  their  reception  upon  the  retina. 

The  study  of  the  subject  has  thus  involved  phenomena, which  can 
be  explained  according  to  well  known  physical  laws.  The  next  step 
is  the  consideration  of  phenomena  of  vision,  that  involve  physiologic 
and  psychologic  conditions. 

By  physiological  conditions,  is  meant  the  recognition  of  form  by 
the  retma,  and  the  transmission  of  the  same  by  the  optic  nerves  to  the 
brain  centres  of  vision.  By  psychologic  phenomena,  we  mean  the 
translation  of  these  nerve  impulses  by  the  brain  into  what  we  term 
sight.  Only  the  first  conditions  come  within  the  scope  of  this  work. 
The  study  of  the  latter  is  commended  to  the  advanced  student  of 
optics  as  being  interesting,  but  unnecessary,  in  his  work. 

The  image  being  formed  upon  the  retina,  which  is  sensitive  to 
light,  certain  nerve  impulses  are  created  and  transmitted  by  the  optic 
nerves  to  the  centers  of  perception  in  the  brain.  These  give  rise  to 
the  senses  of  recognition  of  light,  color  and  form.  The  first  two  may 
be  dismissed  with  a  few  words,  as  they  are  not  embraced  within  the 
limits  of  this  work. 

The  light  sense  is  the  ability  to  recognize  difference  in  the 
intensity  of  light. 

The  color  sense  is  the  ability  to  distinguish  between  different 
colors.     Lack  of  this  sense,  or  a  portion  of  it,  is  called  color  blindness. 

The  most  important  of  all  is  the  form  sense,  that  is,  the  ability  to 
recognize  form. 

Till'  measure  of  the  ability  to  recogntru-  form,  is  called  the  visual 
acuity  of  the  eye. 

For  determination  and  record  of  the  visual  acuity,  some  method 
had  to  be  followed ;  some   standard   by    which  to  measure,    adopted. 


I'  II  V  S  I  O  L  O  G  I  C  A  L         O  1'  T  I  C  S  .  119 

A  single  point  will  make  a  single  retinal  impression;  two  points, 
not  too  close  together, vfiW  be  recognized  separately;  if  they  are  too 
close  to  each  other,  they  may  appear  to  the  eye  as  but  one. 

If  a  straight  line  be  drawn  from  each  of  two  separately  recognized 
points,  through  the  optical  centre  of  the  refracting  system  (the  nodal 
point),  to  the  retina,  they  will  meet  and  cross  each  other  at  the  nodal 
point  forming  an  angle. 

The  smallest  angle  under  which  two  points  may  be  recognized,  is 
the  uicasiire  of  the  visiial  acuity.  In  the  average  normal  eye  this  angle 
has  been  detei  mined  to  be  one  minute,  or  one  sixtieth  of  a  degree. 
A  definition  of  visual  acuity  may  be  given  as: — 

Visual  acuity  is  the  ability  to  recognize  form.  It  depends  upon  the 
anatomical  for  iiiatton  of  the  retina  and  its  sensibility  to  recognize  light 
impulses,  the  ability  of  the  optic  nerve  to  transmit  tliese  impulses,  and 
the  centres  of  vision  to  interpret  them. 

Parallel  lines  of  equal  width,  separated  by  spaces  the  same  width 
as  the  lines, the  width  of  each  line  subtending  an  angle  of  one  minute, 
are  used  as  ests  of  visual  acuity.  Upon  this  principle  the  standard 
te:t  letters  of  Snellen  are  constructed,  the  width  of  each  line  of  the 
letters  is  such  that  two  opposite  points  on  the  line,  subtend  an  angle 
of  one  minute  with  the  nodal  point  of  the  eye. 

To  measure  the  visual  acuity,  it  is  usual  to  measure  the  angle  of 
vision  for  distance;  the  test  type  being  placed  at  least  twenty  feet 
away,  so  that  the  accommodation  may  not  be  called  into  play. 

In  the  formation  of  Snellen's  test  letters,  a  square  thai  subtends 
a  five  minute  angle  is  used  and  this  is  subdivided  into  squares  of  one 
minute  angle  each,  making  twenty  five  in  all.  See  figure  100.  The 
letters  are  formed  upon  the  principle  given  above,  of  three  parallel 
lines  of  equal  width  separated  by  two  spaces  of  the  same  width.  In 
this  manner  each  letter  occupies  a  square  of  five  minute  angle.  At  a 
distance  of  twenty  feet,  a  five  minute  angle  will  include  a  square  of 
about  three-eighths  (g)  of  anjinch,  thejnormal  test  letter  for  twenty  feet 
will  thus  measure  about  tnree-eighihs  of  an  inch  high  and  the  same 
width.  At  forty  feet  the  same  five  minute  angle  will  include  a  square 
of  three  quarters  of  an  inch. 

In  figure  100  the  standard  sizes  of  test  letters  given  are  for  twen- 
ty, thirty,  forty  and  fifty  feet  as  indicated  by  the  number  placed  above 
each  letter. 

The  standard  of  normal  acuity  of  vision  that  has  been  established 
is  not  absolute.  In  some  eyes  the  rods  and  cones  are  placed  more 
closely  together,  and  a  hyper-acute  vision  may  obtain.     It  will  not  be 


I30  OCULAR         RE   F   R  A  C  T  I  O  N. 

uncommon  to  find,  in  testing  eyes  for  visual  acuity,  that  some  can 
recognize  letters  that  are  much  smaller  than  those  that  are  selected 
as  the  standard. 

In  order  to  make  the  measurement  of  the  visual  angle  plain,  let 
figure  loi  represent  an  emmetropic  eye;  P,  its  nodal  point.  At  a  dis- 
tance of  two  hundred  feet  is  located  a  letter  E,  it  occupies  a  square 
of  about  three  and  three-quarters  inches. 


i>o 

m 


Figure 


00 


Principle  upo 
angle  of  one  i 


standard  test  types  are  constructed     eacli  small  square  represents  ae 
the  whole  letter  is  contained  in  a  square  that  subtends  an   angle  of  fiv 
T  represents  the  standard  size  lor  twenty  feet;  the  L,  for  thirty  feet 
the  O,  for  forty  feet  and   the  E  for  fifty  feet. 

From  two  opposite  points,  A  and  B,  on  the  letter,  draw  the 
straight  lines  A  P  and  E  P, through  the  nodal  point  P.  Extend  these 
lines  to  meet  the  retina  at  A'  and  B'.  At  a  distance  of  loo  feet  the 
letter  T  is  placed,  its  size  being  such  that  it  is  just  included  between 
the  lines  A  P  and  B  P.  At  sixty  feet  the  letter  L  is  seen  under  the 
same  conditions,  while  at  forty, thirty  and  twenty  feet  respectively,  are 
placed  the  letters  O,  F  and  C. 

From  the  figure, it  will  be  seen  that  all  of  these  letters  form  upon 
the  retina  the  same  size  image  because  they  are  included  within  the 
same  angle.  The  size  of  the  retinal  images  of  all  these  letters  at  the 
distances  given  is  the  same,  and  is  measured  by  the  distance  between 
the  points  A'  and  B'. 

This  demonstrates  *hat  if  an  eye  can  recognize  a  letter  of  the  size 
of  C  at  twenty  feet,  it  will  be  able  to  recognize  a  letter  of  the  size  of 
E  at  two  hundred  feet,  because  each  forms  the  same  size  retinal  image. 

In  recording  the  visual  acuity,  if  an  eye  can  recognize  the  stan- 
dard letter  for  twenty  feet  at  a  distance  of  twenty  feet,  its  visual 
acuity  is  recorded  as  20/20.  If  at  twenty  feet  an  eye  can  only  recog- 
nize the  standard  letter  for  fifty  feet,  its  visual  acuity  is  recorded  as 
20/50.     The  numerator  of  the  fraction   showing   the  distance  at  which 


PHYSIOLOGICAL         OPTICS. 


M 


^\ ^ 

*a\ i h 

o\ — \ — h 

h  V — \ — is 

"\ — ^ — U 


1  |o  o  s 


?.  p:  s  r  .,  =  ii 


-■Oh. 2^1 


:l8'.^ 


122  OCULAR         REFRACTION. 

the  test  was  made  from  the  card,  the  denominator  of  the  fraction  indi- 
cates the  size  of  standard  test  letters  recognized  by  the  eye  under 
examination. 

The  illumination  of  the  test  card  is  an  important  factor  in  deter- 
mining the  visual  acuity.  The  card  should  be  seen  in  daylight  of 
average  brightness,  or  under  artificial  illumination  equally  as  good. 
No  matter  how  sharp  ones  vision  may  be,  they  cannot  see  in  the  dark. 
The  card  should  have  an  even  amount  of  illumination  throughout  its 
entire  surface. 

Some  refractionisis  have  their  test  cards  brightly  illuminated, 
while  the  patient  is  placed  at  the  required  distance  and  in  compara- 
tive darkness.  Tests  for  visual  acuity  under  these  conditions  are  not 
dependable,  the  lighting  of  the  testmg  room,  when  the  visual  acuity  is 
ascertained,  should  be  uniformly  good  in  order  to  obtain  reliable  data. 


EMMETROPIA. 

The  human  eye  is  a  most  wonderfully  delicate  and  beautiful 
optical  instrument,  and  if  all  eyes  were  perfect,  meeting  all  the  con- 
ditions that  have  been  explained  as  necessary  for  normal  vision,  the 
study  of  its  construction  (structure)  and  the  operation  of  its  functions, 
would  well  repay  any  student 

If  all  eyes  were  emmetropic,  there  would  be  no  need  for  the  opti- 
cian's product;  glasses  (lenses)  would  simply  be  required  to  help  the 
Presbyope,  and  would  merely  consist  of  simple  convex  sphericals,  up 
to  three  dioptres  in  power. 

So  far,  in  the  study  of  Ocular  Refraction,  the  conditions  required 
for  iiorii/a/  I'isivii  only  have  been  explained.  This  is  logical,  for  when 
one  knows,  and  is  able  to  recognize  normal  conditions,  any  departure 
from  the  normal  is   easily    detected. 

It  would  be  supposed  that  abnormal  sight  conditions  would  be 
few,  compared  to  the  many  normal  eyes,  but  facts  that  are  indispu- 
table, prove  the  contrary. 

The  abnormal  sight  conditions  that  may  be  corrected  with  glasses 
(lenses),  are  classed  as  errors  of  refraction,  and  are  embraced  under 
the  one  general  term  Ametropia. 

The  proportion  of  Emmetropic  to  Ametropic  eyes  is  extremely  small. 

Prof.  Helmholtz  said: — "If  an  optician  were  to  bring  to  me  an 
optical  instrument  as  full  of  errors  as  the  average  human  eye,  I  should 
return  it  to  him  as  absolutely  useless."     This  is  perhaps  a  severe  criti- 


1'  II   Y  S   I  O  L  O  G   I   C  A   r,         OPTICS.  123 

cism.  Dr.  Francis  Valk  said: — "  I  believe  that  there  are  very  few 
persons  who  have  perfectly  normal  vision  even  from  their  birth, 
although  perhaps  many  of  them  have  no  trouble  with  their  eyes,  and 
have  always  supposed  their  sight  was  equal  to  that  of  the  perfect 
standard."  This  fact  was  well  demonstrated  a  few  years  ago  by 
Prof.  D.  B.  St.  John  Roosa,  in  an  examination  of  a  number  of  gentle- 
men, all  students,  whose  age  ranged  from  twenty-one  to  thirty-two 
years,  who  had  never  been  conscious  of  any  visual  weakness.  The 
results  of  this  examination  were,  that  only  one  fifth  had  normal  eyes. 
A  more  conservative  statement  t  an  that  of  Prof  Helmholtz,  is 
that  of  M.  Mascart,  who  said:— "The  eye  has  all  possible  defects,  but 
only  to  such  an  extent  that  they  are  not  harmful." 


Figure  102. 

Diagram  to  represent  a  sectional  view  of  an  Emmetropic  eye.     Parallel  rays  of  light,  lying  in 

two  planes  at  light  angles  to  each  other,  are  represented  passing  through  the  refracting  system 

in  its  vertical  and  horizontal  meridians,  and  brought  to  a  focus  upon  the  retina. 

Let  figure  102,  represent  a  sectional  view  of  an  emmetropic  eye. 
The  parallel  lines,  represent  light  rays,  lying  in  two  planes  at  right 
angles  to  each  other,  entering  the  eye  and  brought  to  a  focus  on  the 
retina. 

The  student  may  not  grasp  the  meaning  of  the  expression, — izuo 
pla)ics  at  right  angles  to  each  other, — which  is  so  frequently  used  in 
speaking  of  the  refraction  of  the  eye,  being  equal  or  unequal,  in  two 
meridians,  at  right  angles  to  each  other.  To  make  its  meaning  clear, 
cut  two  pieces  of  card-board  the  size  and  shape  of  I  and  II,  illustrated 
in  figure  103,  that  is,  an  inch  wide  and  four  inches  long;  for  a  distance 
of  two  inches  the  sides  are  parallel,  for  the  other  two  inches,  taperinj 
to  a  point. 


OCULAR 


REFRACTION 


Cut  another  piece  of  card-board  two  inches  square,  see  III,  figure 
103,  and  draw  upon  it  a  circle  P,  an  inch  in  diameter.  Draw  the 
diameters  A.  B.  and  C.  D.  at  right  angles  to  each  other. 

With  a  sharp  knife,  cut  through  the  dotted  lines  indicated  on  I,  as 
X.  Y. ;  on  II,  as  F.  X.  ;  and  III,  as  A.  B.  and  C.  D.  Slip  I  and  II 
together,  and  push  the  four  bladed  point  thus  made,  through  the  cuts 
A.  B.  and  C.  D.  in  the  circle  P,  as  shown  in   IIII,  figure  103 

As  thus  placed,  and  shown  by  IIII,  figure  103,  the  square  card  III 
represents  that  portion  of  the  globe  of  the  eye  surrounding  the  cornea, 
the  circle  P,  represents  the  pupil.  The  two  cards  I  and  II,  represent 
two  bands  of  light  composed  of  parallel  rays,  lying  in  fivo  p/nncs  at 
right  anglfs  to  cacli  otiicr,  they  pass  through  the  pupil  in  the  meridians 
at  90^  and  at  180°,  and  meet  at  the  focus,  or  point  F,  which  is  sup- 
posed to  be  at  the  retina. 

Through  the  aid  of  the  simple  device  just  described,  and  illustra- 
ted by  figure  103, — which  every  student  is  urged  to  make  for  himself, 
— the  condition  of  vision  which  figure  102  is  intended  to  represent, 
will  be  readily  understood.  The  same  idea  will  be  used  to  demon- 
strate the  other  conditions  of  refraction  that  occur  in  the  eye. 

In  figure  102,  the  parallel  rays  traversing  the  two  planes  at  right 
angles  to  each  other,  are  shown  entering  the  emmetropic  eye  in  the 
vertical  and  horizontal  meridians.     As  the  eye  possesses  equal  refrac- 


1 


Figure  103    {Continued i 


./  tage). 


II   Y  S  1  O  L  O  G  I  C  A   I,         OPTIC 


Figure  103.      {Continued'). 


Diagram  to  explain  conslruction  of  card-board  model,  to  represent  a  section  ot  the  eye  sur- 
rounding the  cornea;  the  pupil;  and  rays  of  light  traversing  two  planes  at  right  angles  to  each 
other,  and  entering  the  eye.  From  card-board  of  fair  weight,  cut  the  two  forms  shown  as  I 
and  II,  mark  the  dotted  line  X  Y  on  one,  the  dotted  line  F  X  on  the  other.  Cut  out  another 
form  like  III,  laying  off  the  circle  P,  and  dotted  lines  A  B  and  C  D.  With  a  sharp  knife 
cut  through  the  dotted  lines.     Put  the  model  together  in  the  form  shown  by  IIII. 

tion  in  every  meridian,  these  rays  are  shown  to  converge,  and  focus 
upon  the  retina.  The  eye  is  supposed  to  be  in  a  static  condition,  that 
is,  the  accommodation  is  at  rest,  and  the  eye  is  focussed  for  its  far 


126  O  C   I'   I.  A   K  K  E   F  R  A  C  T   1  O  X  . 

point.  The  dotted  circle  is  supposed  to  pass  through  the  optical  cen- 
tre of  the  refracting  system  and  its  principal  focus:  the  retina  is  seen 
to  be  located  at  its  principal  focus. 


Figure  104. 


Vertical  and  horizontal  meridi 


In  the  beginning  of  the  chapter,  the  statement  is  made,  that  the 
average  emmetropic  eye  possesses  about  +  58. D,  of  refracting  power. 
For  demonstration  purposes,  the  author  will  arbitrarily  assume  that 
an  eye  that  is  emmetropic  will  possess  +  60.  D.  of  refraction. 


/r^° 


Diagram  to  represent  vi 
two  pla 


right  angles  tc 


Figure  105. 


ridians  of  an  ey 


,  and  rays  of  lighi 
;  the  pupil. 


Let  figure  104, represent  the  pupil  of  the  eminetropic  eye, illustra- 
ted by  figure  102.  In  the  vertical  and  horizontal  meridians,  which  are 
represented,  it  will  be  found  to  measure  +  60.  D.  as  shown  in  the 
figure. 

Being  the  equivalent  of  a  spherical  lens,  the  power  of  the  refract- 
ing system  will  be  the  same  in  every  meridian;  for  convenience  and 
simplicity,  the  vertical  and  the  horizontal  meridians  are  selected  for 
demonstration.  It  is  easy  to  remember  that  they  are  at  right  angles 
to  each  other. 


1'  H  V  S  I  O   L  ()  G   I  C  A   L         O   1'  T  I   C  S.  127 

Any  other  two  meridians  at  right  angles,  would  serve  the  same 
purpose,  say; — 75°  and  165°,  or  10°  and  100°, — but  one  has  to  pause 
and  calculate  their  relative  positions. 

Figure  105  may  serve  to  simplify  the  meaning  of  figures  104,  108, 
III  and  114.  The  circle  P  represents  the  pupil,  the  vertical  and  hori- 
zontal meridians  are  designated  as  90°  and  180°,  and  the  light  rays 
traversing   these    meridians   are  also  indicated  by  the  planes  90°  and 


AMETROPIA. 

All  anictropic  eye  may  possess  equal  refract  ion  in  every  meridian, 
but  the  retina  is  not  situated  at  the  principal  focus  of  its  refracting  sys- 
tem under  static  conditions.  Or,  the  refraction  may  not  be  equal  in 
ei'cry  meridian. 

This  definition  is  just  the  opposite  of  that  for  emmetropia,  and  is 
purposely  put  in  this  form  to  make  it  easy  to  remember. 

In  writing  of  the  errors  of  refraction  under  the  title  of  this  chap- 
ter,— "  Physiological  Optics," — the  author  does  not  propose  to  go  into 
the  details  of  their  correction  beyond  an  explanation  of  the  character 
of  the  lenses  required,  and  how  they  affect  the  vision,  by  changing 
the  direction  of  the  rays  of  light  before  they  enter  the  eye. 

The  reason  for  this  is,  that  the  author  does  not  believe  that  the 
student  should  depend  solely  upon  the  writings  or  teachings  of  any 
one  person.  It  gives  the  student  a  more  liberal  education  to  learn 
from  a  number,  besides,  no  one  person  knows  it  all,  nor  is  capable  of 
imparting  his  knowledge  of  every  phase  of  a  subject  equally  well,  so 
that  it  is  wisdom  to  learn  the  views  and  opinions  of  as  many  as  possi- 
ble, upon  a  topic  of  a  scientific  nature. 

The  errors  of  refraction  and  their  correction.is  the  subject-matter 
of  numerous  good  text  books,  the  student  is  referred  to  them  to  study 
in  connection  with  this  work.  A  few  will  be  suggested,  the  author, 
personally,  having  found  them  valuable.  "  Errors  of  Refraction  "  by 
Valk.  "  Physiologic  Optics  "  by  Tscherning.  "  Refraction  "  by  Hart- 
ridge.      "  Refraction  and  How  to  Refract  "  by  Thorington. 

In  the  introduction  to  this  series  of  papers,  written  nearly  a  year 
ago,  this  statement  was  made: 

"  It  is  the  author's  conviction,  that  the  greatest  success  at  present 
is  being  made,  and  in  the  future  will  be  attained,  by  that  class  of 
operators,  who  make  Retinoscopy  the  corner  stone  of  the  adapting  of 
lenses  to  the  correction  of  refractive  errors.     The    aim   of   the    work 


128  O  C    U  L  A   R         R   E  F   R   A  C  T  I  O  N  . 

will,  therefore,  be  to  teach  the  fundamental  principles  of  Retinos- 
copy." 

Since  this  was  written  the  writer  has  undergone  no  "  change  of 
heart,"  buc  is  a  more  enthusiastic  advocate  of  Retinoscopy  than  ever. 
The  subjects  that  have  been  covered  so  far  are  necessary  to  the  study 
in  question,  and  the  remainder  of  this  chapter  is  needed  to  round  out 
the  knowledge  of  the  student,  preparatory  to  taking  up  the  study  of 
Retinoscopy.  This  explanation  is  given,  so  that  the  student  may 
understand  the  writer's  motive.  It  will  also  serve  to  explain  why  the 
errors  of  refraction  of  the  eye,  and  their  corrections,  are  treated  so 
briefly  in  this  chapter. 

In  extenuation,  it  may  be  said,  that  the  most  lengthy  paper  upon 
a  topic  does  not  necessarily  contain  the  most  information.  The  author 
has  endeavored  to  make  the  chapter  on  Physiological  Optics  compre- 
hensive yet  condensed. 

Ametropia  may  be  sub  divided,  and  considered  under  three  heads, 
\\z:--Hyperinetropia,  Myopia  and  Astigniatisiii.  By  some  writers, 
Presbyopia  is  also  considered  as  a  condition  of  Ametropia.  This  is 
hardly  correct,  as  Presbyopia  is  not  an  error  of  refraction,  it  is  due  to 
a  physiological  change  that  takes  place  in  all  eyes  alike.  At  a  certain 
period  in  life,  the  emmetropic,  the  hypermetropic,  the  myopic  and  the 
astigmatic  eye  becomes  presbyopic. 

Presbyopia  should  therefore  be  considered  as  a  separate  and  dis- 
tinct condition  of  refraction.  The  three  phases  of  Ametropia  are 
illustrated  by  figures  io6,  109  and  1 12. 

HYPERMETROPIA. 

Based  upon  the  definition  given  for  emmetropia,  that  for  hyper- 
metropia  is: — 

TIic  Hypermetropic  eye  possesses  equal  refraction  in  every  meridian, 
but  the  retina  is  situated  betiveen  the  refracting  system  and  its  principal 
focus. 

A  number  of  definitions  of  hypermetropia  may  be  given,  but  that 
just  stated,  describes  the  condition  fully  and  in  a  few  words. 

For  comparison,  the  definitions  of  a  few  well  known  authorities 
will  be  quoted. 

"The  hypermetropic  eye  is  too  short.  The  retina  being  too 
Hear  the  optic  system,  the  hypermetrope  cannot,  without  an  effort  of 
the  accommodation,  reunite  on  the  retina  parallel  or  diverging  rays." 
Tscherning. 


PHYSIOLOGICAL        OPTICS.  129 

"  Hypermetropia  may  be  defined  as  a  condition  in  which  the 
anteroposterior  axis  of  the  eyeball  is  so  short,  or  the  refracting  pow- 
er so  low,  that  parallel  rays  are  brought  to  a  focus  behind  the  retina 
(the  accommodation  being  at  rest).  In  other  words,  the  focal  length 
of  the  refracting  media  is  greater  than  the  length  of  the  eyeball." 
Hartridge. 

"  It  is  characterized  by  the  fact,  that  the  retina  is  situated  be- 
tween the  dioptric  system  and  the  principal  focus  of  the  eve. "  Lajidolt. 

"  The  hypermetropic  eye  is  one  which  in  a  state  of  rest,  requires 
convergent  rays,  in  order  to  be  able  to  focus  them  upon  the  retina." 
Landolt. 


Figure  106. 

Sectional  view  of  a  hypermetropic  eye  represented  by  diagram.     Parallel  rays  of  light,  lying 
in  two  planes  at  right  angles  to  each  other,  are  shown  passing  through  the  refracting  system 
in  the  vertical  and  horizontal  meridians,  and  brought  to  a  focus  behind  the  retina.     The  dot- 
ted circle  is  supposed  to  pass  through  the  principal  focus, 

"  A  hypermetropic  eye  is  one  whichj  in  order  to  see  distinctly  at 
a  distance,  requires  a  convex  glass."     Landolt. 

All  of  these  statements  should  be  carefully  studied,  for  while  they 
vary  in  describing  the  same  condition,  they  may  be  resolved  into  the 
same  thing.  They,  however,  present  the  subject  from  various  view 
points,  and  comparisons  are  always  valuable  in  the  acquiring  of 
knowledge. 

Analyzing  the  author's  definition,  it  will  be  found  that  it  explains 
not  only  the  conditions  that  exist,  but  also  indicates  their  correction 
to  the  student  who  has  mastered  Physical  Optics. 


If  its  refracting  system  possesses  equal  refraction  in  every  meri- 
dian, it  is  capable  of  creating  a  correct  image,  if  the  retina  be  situated 
at  its  principal  focus.  As  the  retina  is  too  near  to  the  refracting  sys- 
tem, being  inside  of  its  principal  focus,  the  principal  focus  must  be 
made  shorter  by  increasing  the  refraction.  This  indicates  the  addition 
of  a  convex  spherical  lens. 

Tkc  correction  for  Hypermetropia  is  a  convex  spherical  lens  of  such 
power,  tliat  combined  ivitii  the  rcf->-actiug  system  of  the  eye,  their  prin- 
cipal focus  will  be  upon  the  retina. 

L,et  figure  io6  represent  a  sectional  view  of  a  hypermetropic 
eye.  In  the  vertical  and  horizontal  planes,  parallel  rays  of  light  are 
seen  to  enter  the  eye,  which  is  in  a  state  of  rest,  and  their  principal 
focus,  indicated  on  the  dotted  circle,  is  behind  the  retina.  On  the 
retina  they  are  seen  to  create  a  diffused  circle,  and  therefore  accord- 
ing to  physical  optics,  they  create  no  clear  image. 

Read  the  definition  of  hypermetropia  again,  and  study  this  dia- 
gram to  see  what  it  means.  It  will  also  explain  the  definitions  of 
-Tschcrning;  Hart  ridge  and  Landoll. 


■•_  Figure  107. 

Diagram  to  represent  the  correction  for  Hypermetropia.     Tlie   ctnyex   spherical   lens  giv( 
th'e  parallel  rays  sufficient  convergence  before  entering  the   eye,  to   cause  them  to  focus  upo 


In  figure  107,  this  hypermetropic  eye  is  illustrated  with  its  correc- 
tion before  it.  As  it  is  only  adapted  for  convergent  rays  when  its 
accommodation  is  relaxed,  the  required  convex  sphericallens  is  shown 
imposed,  changing  the  parallel  rays  to  convergent  rays  as  they  enter 
the  eye,  so  that  they  are  now  brought  to  a  focus  upon  the  retina. 


I'  H  \-  S  I  O   I.  O  G  I  C  A 


OPTICS. 


131 


In  figure  108,  I,  represents  the  pupil  of  this  hypermetropic  eye, 
ts  meridians  measure  -f-  57-  D.  II  represents  its  correction,  a  -(-  3.00 
D,  spherical  lens;  the  +  3.00  D.  added  to  the  +  57.  D.  of  the  eye 
equals. the  theoretical  emmetropia  of  +  60.  D. 

In  the  correction  of  hypermetropia,  it  may  be  found  that  the 
visual  acuity  may,  or  may  not  be  normal;  it  is  not  infrequent  to  find 
vision  hyper-acute,  being  above  the  normal  acuity.  Of  course  it  is 
obtained  through  an  effort  of  the  accommodation. 

When  the  vision  is  below  normal  in  hypermetropia,  a  full  cor- 
rection]does  not  always  raise  the  vision  to  the  normal  acuity. 


Figure  108. 


iof:T.ooD. 


<i  a  liypermelropic  eye  h£ 
)  correct  ils  error.      The  I 


'g+  57. D. 
I  combined 
t-  60.  1). 


of  refraction,  and  a  convex  splK 
represent  the  arbitrary  emmeti 


In  the  wearing  of  a  correction  for  hypermetropia,  it  is  not  alivays 
a  question  of  the  visual  acuity  that  is  involved,  but  one  of  relief  for 
the  accommodation. 

Vision  may  be  up  to  the  normal  acuity,  or  even  be  hyper-acute, 
without  the  correction  of  the  hypermetropia,  but  the  accommodation 
is  required  to  be  exerted  to  obtain  this  result,  causing  nervous  strain 
and  ocular  distress.  Ocular  headaches  are  freqrjently  caused  by  this 
condition,  and  are  therefore  relieved  by  wearing  the  correction. 

'Under  tlicsc  conditions,  it  is  not  a  question  of  lohat  one  can  see,  but 
luno  niiie/i  effort  is  exerted  to  see,  and  its  eonscquenees. 

The  correction  for  hypermetropia  is  the  strongest  convex  spheri- 
cal that  will  permit  of  the  best  visual  acuity.  A  weaker  spherical  than 
is  thus  indicated,  requires  that  the  accommodation  shall  supply  the 
difference.  A  stronger  spherical  than  indicated,  will  create  an  artifi- 
cial rnyopia,  and  thus  blur  the  distant  vision.. 


132  ()  C    r    I.  A  R         R   E  F   R  A  C  T  I  O  N  . 

The  Hypermetrope  is  compelled  to  use  his  accommodation,  to 
correct  his  refractive  error,  in  order  to  see  distant  objects  distinctly. 
By  reason  of  the  natural  association  of  convergence  to  accommoda- 
tion, when  he  accommoda.es,  the  tendency  is  also  to  converge.  This 
causes  disturbance,  and  he  must  do  one  of  two  things  ;  either  dis- 
associate convergence,  which  is  likely  to  cause  eye  strain,  or  mentally 
suppress  vision  in  one  eye,  which,  of  course.destroys  binocular  vision. 

If  lie  cannot  accommodate  for  distance,  zvithout  also  converging,  his 
visual  lines  ivill  meet  at  a  point  nearer  than  the  object  upomvliich  liis 
vision  is  ''fixed,"  and  lie  can  thus  only  see  it  ivith  one  eye 

Double  vision  would,  under  these  circumstances,  be  had,  but 
nature  comes  to  the  rescue,  and  he  learns  to  mentally  suppi-ess  the 
vision  in  one  eye. 

It  is  this  condition  that  causes  convergent  strabismus  or  cross  eyes. 

The  importance  ofearly  in  life  correcting  Hypermetropia  is  thus 
demonstrated  if  there  is  any  tendency  to  the  above  conditions. 
Glasses  do  not  cure  cross  eyes,  neither  do  prisms  ;  lenses  merely  correct 
the  error  of  refraction  and  remove  the  cause. 

Convergent  strabismus  is  an  unfailing  sign  of  lack  of  the  exercise 
of  the  function  of  vision  in  the  deviating  eye.  The  prevention  of 
convergent  strabismus  thus  means,  in  many  cases,  the  saving  of  the 
sight  of  the  eye. 

The  term  Amblyopic  is  applied  to  the  deviating  eye. 

The  hypermetropic  eye  is  popularly  called  a  ''far  sighted  eye  "  a 
better  and  more  correct  term  would  be  a  zveak  sighted  eye,  because  it 
is  lacking  in  sufficient  refraction. 

MYOPIA. 

In  giving  a  definition  of  Myopia,  the  same  basis  will  be  used  as  in 
definins  Hypermetropia.     Accordingly  :-- 

The  Myopic  eye  possesses  equal  refraction  in  every  meridian,  but 
the  retina  is  situated  beyond  the  principal  focus  of  its  refracting  system. 

It  will  be  seen,  by  comparison  of  the  definition  of  myopia  with 
that  of  hypermetropia,  that  they  are  just  the  opposite. 

In  describing  myopia,  Landolt  speaks  of  it  as  axial  myopia,  indi- 
cating that  in  the  majority  of  the  cases,  that  the  axial  length  of  the 
eye,  along  its  antero-posterior  diameter,  is  too  great. 

Tschcrning  also  makes  use  of  the  terms  axial  myopia  and  axial 
hypermetropia,  and  states  that  a  departure  of  one  millimeter  in  length 
from  emmetiopia  requires  two  and  a  half  dioptres  of  correction.     Ac- 


I 


cording  to  this  rule,  one  may  estimate    the  abnormal    lengthening  of 
a  myopic  eye. 


Myopia,  represented  by  d 
are  brought  to  a  focus  in  ti 


eye.     Parallel  rays  of  light 
rcle  passing  through  the  principal 


The  correction  of  Myopia  is  a  concave  spherical  lens  of  such  poivei\ 
that  couthincd  ivith  the  refracting  system  of  the  eye,  their  principal 
focus  ivill  be  upon  the  retina. 


The  correction  of  Myopia  represented  by  diagram      The  paralli 
divergence,  by  the  imposed  concave  spherical  lens,  to  enable  the 


Let  figure  109  represent  a  sectional  view  of  a  myopic  eye,  the 
parallel  rays  of  light  are  seen  to  converge  at  the  principal  focus,  which 
is  in  front  of  the  retina,  and  then  diverge  to  reach  the  retina  as  a 
diffused  circle.     This  is  a  typical  case  of  axial  myopia,  the  dotted  cir- 


134  O  C   U   I.   A   R  REFRACTION. 

cle,  passing  through  the  optic  centre  of  the  refracting  system  and  its 
principal  focus,  indicates  the  lengthening  of  the  globe  of  the  eye. 

Figure  i  lo  is  intended  to  show  how  the  correcting  lens  affects 
the  parallel  rays;  being  a  concave  lens  it  causes  them  to  diverge,  and 
as  the  myopic  eye  has  too  short  a  focus  for  its  length,  if  the  concave 
lens  is  correctly  adapted,  the  divergent  rays  are  brought  to  a  focus 
upon  the  retina. 

In  figure  in,  I,  represents  the  pupil  of  this  myopic  eye,  the  mer- 
idians represented  measure  +  66.  D.  II.  is  its  correction,  a  —  6.00  D. 
spherical  lens.  The  two  combined  represent  theoretical  emme- 
tropia  of  -)-  60  D. 


Figure  III. 

Two  nieridiansol  a  Myopic  eye,  having  +  66.  D.  of  refraction,  illustrated  by  I,  tlie  —  6.  D. 
spherical  to  correct  the  error  shown  by  II. 

In  myopia  the  visual  acuity  is  below  normal  for  distance,  even 
when  the  error  is  small  It  differs  from  hypermetropia  in  this 
respect.  The  reason  for  this  is,  that  in  hypermetropia  the  refraction 
that  is  lacking  may  be  supplied  by  the  accommodation,  the  eye  thus 
has  the  power  to  increase  its  refraction  and  obtain  a  normal  visual 
acuity  by  an  effort.  There  is  no  power  in  the  eye,  however,  by  which 
it  can  reduce  its  refracting  power,  hence,  in  myopia,  the  visual  acuity 
is  lacking. 

In  the  wearing  of  a  correction  for  myopia,  //  is  a  question  of  the 
visual  acuity  that  is  involved. 

The  correction  for  myopia  is  the  weakest  concave  spherical  that 
will  permit  of  the  best  visual  acuity,  which  may,  or  may  not,  be  the 
normal  acuity. 

A  full  correction  in  myopia  does  not  always  raise  vision  to  normal. 
In  high  degrees  a  full  correction  will  not  always  be  tolerated. 


P  H  Y  S  I  O  L  O  C,  I  C  A   L         O  P  T  I  C  S.  135 

There  has  been  much  discussion  of  the  advisibility  of  giving  a 
full  correction  in  myopia;  and,  judging  from  the  number  of  myopes 
who  are  wearing  an  under  correction,  it  would  seem  that  there  is  a 
ettled  policy  of  giving  under  corrections. 

The  object  of  correcting  errors  of  refraction  is  to  adapt  such  a 
lens  to  each  eye  as  will,  as  nearly  as  possible,  create  artificial  emme- 
tropia,  no  means  of  restoring,  or  creating  natural  emmetropia,  when 
it  does  not  exist,  having  been  evolved  by  the  ophthalmic  surgeon  or 
the  oculist  up  to  the  present  writing.  There  is  no  telling  what  they 
may  do  in  the  future;  however,  we  are  at  present  dependent  upon 
mechanical  devices  to  simulate  emmetropic  conditions. 

A  full  correction  is,  therefore,  the  ideal  correction,  and  the 
writer  believes  that  in  the  great  majority  of  cases,  tlic properly  adapt- 
ed lens  ivill  he  aeeepted. 

(Anisometropia  and  pathological  conditions  excepted). 

No  one  would  think  of  using  a  crutch  that  is  too  short,  in  prefer- 
ence to  one  of  the  proper  length.  Glasses  are  like  crutches,  a  me- 
chanical means  to  an  end. 

The  greatest  cause  of  dissatisfaction  is  inaccurately  adapted  cor- 
rections. 

In  the  correction  of  myopia,  it  must  be  remembered,  that  the 
visual  lines  of  the  uncorrected  or  under- corrected  myope  have  never 
been  parallel,  but  always  converged. 

A  full  correction,  creating  parallelism,  therefore,  involves  a  re- 
adjustment of  the  relations  of  accommodation  and  convergence,  just 
the  same  as  in  the  correction  of  hypermetropia. 

A  Myope  is  commonly  described  as  near-sighted,  and  the  term 
indicates  his  inability  te  see  objects  at  a  distance,  while  the  vision  for 
near  objects  may  be  extremely  good.  In  fact,  the  myope  has  a  more 
acute  vision  for  near  point  than  either  the  Emmetrope  or  the  Hyper- 
metrope. 

ASTIGMATISM. 

Pn  an  astigniatie  eye  the  refraetion  is  unequal  in  various  nieridians. 

This  definition  indicates  that  the  lens  for  the  correction  of  astig- 
matism must  possess  unequal  refraction  in  its  various  meridians. 
Su^h  lenses,  the  student  knows,  are  cylinders,  or  cylinders  combined 
with  sphericals.  An  astigmatic  eye,  like  an  astigmatic  lens,  has  two 
principal  meridians,  which  are  always  at  right  angles  to  each  other. 
The  meridians  of  greatest  and  least  refraction  of  the  eye  are  thus  at 
right  angles. 


136  OCULAR  R   E   K   R  A  C  T   I  O  N. 

Three  different  conditions  may  exist  to  cause  astigmatism. 

First:— In  one  of  the  principal  meridians  of  the  eye,  parallel  rays 
of  lighi  may  focus  upon  the  retina,  in  the  other  principal  meridian, 
they  focus  behind  the  retina. 

This  condition  is  called  simple  hypernictropic  astigiiiatisut.  Its 
correction  is  a  planoconvex  cylinder,  the  axis  being  located  so  that  the 
parallel  rays  that  focus  upon  the  retina,  are  not  refracted  in  passing 
through  the  lens,  but  those  at  right  angles  to  the  axis,  aie  converged 
sufficiently  for  the  eye  to  focus  them  upon  the  retina. 

Second: — In  one  of  the  principal  meridians  of  the  eye,  parallel 
light  rays  may  focus  upon  the  retina,  in  the  other  principal  meridian 
they  focus  before  the  retina. 


Figure  i 


of  an  AsligiTiatic  eye.  illustrated  by  diagram.      Parallel   rays  traversing  the 
,  focus  behind  the  retina;  those  in  the  horizontal  meridian,  focus  before  the 


retina.     The  effect  is  hypernietropia  in  the  vertical,  myopia  in  the  horizontal  pla 

This  is  termed  simple  myopic  astigmatism.  The  correction  for 
this  condition  of  refractive  error  is  a  planoconcave  cylinder.  The 
a,\is  placed  so  that  it  permits  those  parallel  rays  that  the  eye  is  capa- 
ble of  bringing  to  a  focus  upon  the  retina,  to  pass  undisturbed.  At 
right  angles  to  the  axis,  it  causes  the  parallel  rays  to  diverge  to  the 
degree  necessary  for  the  eye  to  bring  them  to  a  focus  also  upon  the 
retina. 

Third:— In  one  of  the  principal  meridians  of  the  eye  parallel  rays 
of  light  are  brought  to  a  focus  before  the  retina,  in  the  other  princi- 
pal meridian,  behind  the  retina. 

To  this  condition  of  refraction  the  term  compound  astigmatism  is 
given.      In  one  of  the  principal    meridians  a  hypermetropic  cimduion 


exists  while  in  the  other  a  myopic  condition  obtains.  The  correction 
for  compound  astigmatism  is  therefore  a  piano  convex  cylinder  com- 
bined with  a  piano  concave  cylinder,  their  axes  being  at  right  angles 
to  each  othei-,and  located  in  the  required  positions  as  described  in  the 
correction  of  simple  hypermetropic  and  simple  myopic  astigmatic  error. 
It  will  be  remembered  that  contra-generic  cross  cylinders  may  be 
transposed  into  equivalent  spherocylinder  lenses,  therefore,  com- 
pound   astigmatic  corrections    may  be  made  by  contra-generic  cross 


Figure  113. 

Utigmatism  illustrated.      The  concave  cylinder  gives  a  divergence  to  tlie 
parallel  rays  in  the  horizontal  meridiat-..  while  in  the  vertical  meridian   they  pass  uiialTected. 
The  convex  spheric  il   lens  then  changes  the  parallel  rays  in  the  vertical   meridian  to  con- 
vergent ray>,  and  reduces  the  divergency  ot  those  in  the  horizontal  meridian  sufficiently  for 
the  eye  to  focus  them  all  upon  the  retin  i. 

cylinders,  axes  at  right  angles;  by  a  convex  spherical,  combined  with 
a  concave  cylinder;  or,  by  a  concave  spherical  combined  with  a  con- 
vex cylinder 

Figure  1 12  represents  a  sectional  view  of  an  eye  In  which  a  com- 
pound astigmatic  condition  exists.  Parallel  rays  in  the  vertical  mer- 
idian are  brought  to  a  focus  behind  the  retina,  showing  that  in  this 
meridian  the  eye  does  not  possess  sufficient  refraction.  In  the  hori- 
zontal meridian,  the  parallel  rays  focus  before  the  retina,  too  much 
refraction  existing  through  this  meridian. 

Figure  113  illustrates  the  correction  of  the  condition  depicted  in 
figure  112,  the  correction  being  made  with  a  convex  spherical  lens 
combined  with  a  concave  cylinder. 

First,  the  convex  spherical  is  imposed,  this  corrects  the  hyperme- 
tropia  in  the  vertical  meridian,  but  increases  the  tnyopia  in  the   hori- 


I3S 


R  A  C  T 


zontal.  Next,  the  concave  cylinder  is  imposed,  axis  vertical,  to 
correct  the  myopia. 

In  figure  114,  I  represents  the  pupil  of  a  compound  astigmatic 
eye.  In  the  vertical  meridian  the  refraction  measures  +  58.  D.,  in 
the  horizontal  meridian,  +  62.  D.  II  represents  a  conve.x  spherical 
lens  of  2  00  D.  Ill  represents  a  concave  cylinder  of  4.00  D.,  the 
axis  being  vertical.  The  two  lenses  in  the  positions  designated,  com- 
bined with  the  refracting  system  of  the  eye  equals  +  60.  D.  in  every 
meriilian,  or  the  theoretical  emmetropia. 

To  represent  astigmatism  with  the  model  shown  in  figure  103, 
cut  one  of  the  tapered  points,  either  I.  or  II.,  a  bit  shorter  than  the 
other. 


Figure 


The  principal  meridians  of  an  astigmatic  eye;  the  vertica'.  nieasur 
lal.  -I-  62.  D.,  illustrated  by  diagram  I      The  convex  spherical  of 

nder  of  —  4  00  D.  axis  90'  is  shown  by  III. 

Lem  of  tlie  eye,  equal  the  arbitrary  emmetr 
meridian. 


by 


II;  the  concave  1 
h  the  retracting 


ng  +58  D  .  the  horizon- 
+  2. CO  D  is  represented 
The  two  lenses,  combined 
)pia  of  +  60.  U.  in  every 


In  Astigmatism,  the  wearing  of  a  correction  involves  both  visual 
acuity  and  effort  of  accommodation. 

The  astigmatic  person  frequently  considers  that  he  is  near  sight- 
ed, because  by  holding  small  objects,  notably  fine  print,  closer  to  the 
eyes  than  the  customary  reading  distance,  he  is  enabled  to  see  more 
distinctly. 

By  so  doing  he  creates  a  larger  retinal  impression  and  is  thus  en- 
abled to  see  more  easily. 

In  the  majority  of  cases  of  astigmatism,  when  a  convex  cylinder  is 
required  for  correction,  the  axis  will  be  found  to  be  at  or  near  the 
vertical  meridian.  If  concave  cylinders  are  required,  the  axis  will 
be  at  or  near  the  horizontal  meridian. 


PHYSIOLOGICAL         OPTICS.  i39 

Such  corrections  are  said  to  be  according  to  the  rule.  If  convex 
cylinders  are  required  at  or  near  the  horizontal  meridian,  or,  concave 
cylinders  at  or  near  the  vertical,  they  are  said  to  be  against  the  rule. 

Astigmatism  against  the  rule  creates  poorer  vision  than  astigma- 
tism with  the  rule,  though  the  error  may  be  of  like  degree  in  both  in- 
stances. 

It  is  not  uncommon  to  find  that  the  axis  of  the  correcting  cylind- 
er for  one  eye  will  be  in  either  the  vertical  or  horizontal  meridian, 
while  for  the  other  eye  it  will  be  in  a  meridian  at  an  oblique  angle  to 
the  other. 

This  is  termed  Assymnietry  of  the  axes. 

If  the  correcting  cylinders  are  of  the  same  species,  and  both  are 
required  in  the  vertical,  or  both  in  the  horizontal  meridian,  they  are 
said  to  be  symmetrical.  Cylinders  of  the  same  species,  that  are  re- 
quired in  meridians  that  deviate  np  from  the  horizontal  to  the  same 
degree,  or  doivn  from  the  horizontal  to  the  same  degree,  are  also  said 
to  be  symmetrical  corrections. 

Corrections  for  astigmatic  errors,  where  the  axes  are  symmetri- 
cal, will  be  more  readily  tolerated  and  accepted,  than  when  the  axes 
are  not  symmetrical.  In  cases  of  assymmetry,  it  may  be  necessary  to 
follow  a  proce   ure  in  correction  similar  to  that  in  Anisometropia. 

A  comparison  of  the  various  conditions  of  Ametropia,  with  Em- 
metropia,  will  show  that  in  a  static  condition  the  emmetropic  eye  ts 
adapted  for  parallel  liglit  rays;  the  hypermetropic  eye  for  convergent 
rays;  t lie  myopic  eye  for  divergent  rays.  The  Astigmatic  eye  is  adapted 
to  convergent  and  divergent  rays;  or,  parallel  and  divergent  rays  :  or, 
parallel  and  convergent  rays. 

PRESBYOPIA. 

Presbyopia  is  not  an  error  of  refraction  It  is  a  physiological  change 
that  occurs  in  the  eye,  resulting  in  the  impairment  of  one  of  its  functions. 

It  is  a  loss  of  the  power  of  accommodation,  which  is  gradual  and 
progressive,  and  when  the  Emmetrope  finds  that  he  is  unable  to 
accommodate  sufficiently  to  allow  him  to  read  comfortably  at  his 
accustomed  reading-distance,   presbyopia  is  said  to  have  set  in. 

Presbyopia  is  that  condition  in  which  there  is  a  manifest  inability  of  an 
eye  to  accommodate  for  a  near  point  of  nine  or  ten  inches. 

It  is  usual  to  find  that  Presbyopia  begins  about  the  age  of  thirty- 
eight  to  forty-two  years.  Some  authorities  state  that  it  is  due  to  a 
hardening  of  the  crystalline  lens;    others,  to  a  weakening  of  the  cili- 


140  OCULAR         REFRACTION, 

ary  muscles;  still  others,  to  the  two  conditions  combined.  Any  one 
of  the  three  causes  is  acceptable,  to  all  intents  and  purposes,  they  are 
but  different  ways  of  stating  the  same  thing. 

It  is  not  the  writer's  intention  to  go  very  fully  into  the  subject, 
as  it  has  been  so  well  treated  in  numberless  works.  One  point,  how- 
ever, will  be  emphasized.  Presbyopia  and  hypermetropia  are  some- 
times confused,  because  the  correction  for  hypermetropia  is  a  conve.x 
spherical  lens,  while  a  convex  spherical  lens  also  compensates  for  the 
loss  of  accommodation  in  presbyopia.  Tlicy  arc  separate  and  distinct 
conditions. 

In  giving  a  lens  to  compensate  for  presbyopia,  any  errors  of 
refraction  must  first  be  corrected,  and  the  presbyopic  addition  made 
to  the  correction.  All  eyes  are  affected  by  presbyopic  conditions 
after  about  the  age  indicated  above.  The  Emmetrope  begins  to  use 
a  convex  spherical  glass.  The  Hypermetrope  requires  a  stronger 
convex  spherical  for  reading  than  for  the  correction  of  his  erro'-. 
The  myope  requires  a  ivcaker  concave  spherical  for  reading  tlian  for 
distance;  he  may  need  no  lens  whatever  for  reading;  or,  he  may 
require  a  convex  spherical  for  reading.  It  is  dependent  upon  the 
degree  of  the  myopia  and  the  progress  of  the  presbyopia.  The  astig- 
matic glass  wearer  requires  a  convex  spnerical  added  ot  his  cylindri 
cal  correction      The  definition  by  Bonders  is: — 

"  The  term  presbyopia  is  therefore  to  be  restricted  to  the  condi 
tion  in  which,  as  the  result  of  the  increase  of  years,  the  range  (f 
accommodation  is  diminished,  and  the  vision  for  near  objects  is 
interfered  with.  For  its  correction  it  requires  a  convex  lens  of  suita- 
ble power  "  According  to  Bonders,  the  following  table  of  the  ampli- 
tude of  accommodation  according  to  age  is  correct. 
Age.  Amplitude   (Power) 

lo  1  5  oo  Dioptres 

12  14  oo         " 

15  12.00         " 

20  lO-So         " 

25  g.oo         " 

30  7-5° 

35  6  00 

40  4-5° 

45  350 

SO  2-5° 

55  1-50 

60  1. 00         ' 


The  customary  distance  for  the  average  reader  to  hold  his  paper 
or  book,  is  about  fourteen  to  sixteen  inches,  and  so  long  as  one  has 
five  dioptres  of  accommodation  at  his  command,  he  has  no  difficulty. 
It  is  not  possible  to  use  the  whole  amount  of  accommodation  one 
possesses,  for  any  prolonged  period;  only  a  certain  proportion  being 
available. 

The  following  table  will  be  found  to  apply  in  the  majority  of 
cases. 

Age.  Presbyopic  Addition 


40 

+  0.50  D 

optres 

45 

+  1.00 

50 

-j-  2.00 

52 

+   2- 25 

55 

+    2-50 

" 

58 

+  3°o 

" 

ANISOMETROPIA. 

The  term  Anisometropia  strictly  applies  to  any  difference  in  the 
refraction  of  two  associated  eyes.  It  is  usual,  however,  to  infer  that 
there  is  a  marked  difference,  the  term  being  rarely  used  unless  the 
difference  is  greater  than  one  dioptre.  It  is  usually  applied  to  de- 
scribe the  condition  of  vision  in  which  error  of  refraction  occurs  in 
both  eyes,  but  of  a  markedly  different  degree  of  the  same  kind,  or  a 
difference  in  the  character  of  the  error.  It,  however,  may  be  quite 
properly  used  where  normal  refraction  occurs  in  one  eye,  while  an 
error  of  refraction  exists  in  the  other. 

In  cases  of  anisometropia,  the  visual  acuity  of  one  eye  is  apt  to 
be  less  acute  than  the  other,  and  the  one  having  the  better  vision  is 
said  to  be  the  "  douiinant  eye." 

When  anisometropia  occurs,  and  the  errors  are  not  corrected, 
binocular  vision  may  not  exist. 

The  following  procedure  in  the  correction  of  the  condition  will  be 
necessary. 

If  it  is  found  there  is  a  marked  difference  in  the  visual  acuity  of 
one  eye  compared  to  the  other,  make  a  note  of  the  one  in  which  the 
best  vision  obtains,  and  give  such  eye  the  credit  of  being  the  domin- 
ant one. 

Give  full  correction  for  the  dominant  eye,  and  go  as  far  as  pos- 
sible toward  a  full  correction  for  the  other  as  will  be  consistent  with 
comfortable  binocular  vision. 


142  U  C   U   L  A  R         R   E    F    R  A  C   T   I  O  N. 

A  s:ife  rule  to  follow  in  such  cases  will  be  to  make  a  difference  of 
not  more  than  two  to  three  dioptres  in  the  corrections.  The  reason 
for  this  may  readily  be  demonstrated.  With  a  convex  lens  of  eight 
dioptres,  and  one  of  five  dioptres,  create  two  images  of  the  same  ob- 
ject upon  the  same  screen,  side  by  side  ;  it  will  be  seen  that  the 
stronger  lens  creates  the  smaller  image.  It  is  this  difterence  in 
the  size  of  the  retinal  images  that  cannot  be  tolerated. 

Where  a  high  degree  of  astigmatism  e.xists,  and  the  axes  of  the 
correcting  cylinders  are  not  symmetrically  located,  it  will  not  always 
be  possible  to  give  a  full  correction  for  the  error  for  both  eyes.  A 
full  correction  may  be  given  the  dominant  eye,  while  a  portion  of  the 
cylinder  correction  may  be  given  its  mate;  in  some  instances  the 
cylinder  will  have  to  be  omitted  for  the  poor  eye  ;  in  some  cases  the 
cylinders  will  not  be  accepted  for  either  eye. 

ASTHENOPIA. 

The  term  Asthenopia  is  derived  from  the  word  asthenia,  meaning 
weakness  ;  without  strength.  Asthenopia  means  weakness  of  the 
eyes,  as  manifest  by  an  effort  to  see,  more  particularly,  when  applied 
continuously    to  near   work,    such    as   reading,   sewing,  etc.. 

Asthenopia  may  be  divided  into  two  classes,  accommodative  and 
mu  cular.  The  first,  is  caused  by  a  strain  on  the  ciliary  muscles,  and 
may  be  traced  to  an  excessive  effort  of  tlie  accommodation  to  over- 
come hypermetropia  or  astigmatism.  The  second,  is  caused  by  an 
imbalance  of  the  motor  muscles  of  the  eyes,  so  that  binocular  vision 
is  maintained  with  an  effort 

Asthenopia  in  either  case  may  be  designated  as  a'muscular  weak- 
ness, affecting  the  action  of  accommodation  and  convergence,  which 
are  intimately  associated  and  dependent  upon  each  other.  Asthen- 
opia is  indicated  when  frontal  headaches  occur,  when  the  print 
blurs,  and  the  words  run  together.  The  person  rnay  close  the  eyes, 
and,  after  resting  a  bit,  resume  his  occupation  for  a  short  time,  when 
the  phenomena  will  again  recur.  Sometimes  actual  pain  will  be  felt 
in  one  or  both  eyes,  that  becomes  more  and  more  acute  as  the  eyes 
are  forced  to  continue  their  labor.  There  may  a.lso  be,  an  intolerance 
to  light  to  more  or  less  degree.  ,     '  ,..,,,, 

Asthenopia  must  not  be  confounded  with  tliose  cases  in  which  no 
ametropia  or  imbalance  of  the  motor  muscles  exist;  yet  the  person 
will  complain  of  some  or  all  of  the  symptoms  given.  There  is  a  limit 
to  the  endurance  of  all  parts  of  the  body,  and    when    that    is   reached 


P  H   V  S   I  O    I,  O  G   t  C  A   L  op  T   I  C  3.  143 

nature  rebels.  One  may  be  possessed  of  absolute  mental  and  physi- 
cal perfection,  yet  if  either  be  overtaxed,  there  is  certain  to  be  proof 
of  it. 

Some  people  are  unreasonable  with  themselves  in  this  respect, and 
expect  too  much.  This  is  particularly  the  case  with  the  eyes.  They 
are  abused  by  the  great  majority,  and  th  ;  conditions  of  modern  liv- 
ing are  making  more  and  greater  demands  upon  the  eyes. 

This  same  unreasonableness  is  shown  by  many  who  are  given 
glasses  to  correct  some  error  of  refraction.  The  glasses  may  bring 
very  poor  vision  up  to  normal,  affording  the  wearer  visual  comfort 
within  reasonable  limitations,  yet  they  expect  and  demand  more  than 
could  be  expected  if  they  were  gifted  with  emmetropic  eyes. 

By  many  refractionists,  both  oculists  and  opticians,  the  prescrib- 
ing of  weak  power  lenses  is  not  advocated,  they  argue  that  errors  of 
low  degree  may  and  should  be  ignored,  that  the  eye  strain  in  such 
cases  may  be  traced  to  some  deeper  cause.  This  may  be  true  to  a 
certain  extent.  Myopia  of  a  dioptre  or  so  rarely  causes  trouble 
enoug  1  to  drive  the  person  to  the  ocular  refractionist,  but  by  com- 
parison of  distant  vision  with  some  friend  they  may  learn  their  de- 
ficiency and  seek  a  correction.  Hypermetropia  may  e.xist  to  a  like 
amount  in  both  eyes  and  to  quite  a  considerable  amount  without 
causing  trouble.  It  is  now  acknowledged  that  small  errors  of  refrac- 
tion uncorrected,  and  higher  errors  under-corrected,  are  frequently 
the  cause  of  asthenopic  conditions  of  vision. 

Again,  it  will  be  frequent  to  find  that  anisometropia  of  a  high  de- 
gree may  exist;  yet  there  will  be  no  marked  asthenopic  symptoms. 

The  majority  of  persons  who  suffer  from  true  asthenopia,  or  "eye 
strain,"  are  young  people,  that  is,  under  the  age  of  thirty.  It  will  be 
noted  that  the  error  of  refraction  is  small  in  both  eyes,  but  differing 
in  kind  or  degree ;  or  that  one  eye  may  be  emmetropic,  while  the 
other  has  a  small  error. 

This  is  really  the  secret  of  the  whole  trouble,  the  difference  in 
the  small  errors.  They  may  be  classed  as  anisometropia  of  low  de- 
gree. The  reason  that  asthenopia  is  developed  is,  that  as  the  error 
is  small  in  one  or  both  eyes,  that  fairly  good  or  even  normal  vision 
exists  in  both;  therefore,  binocular  vision  is  desired  and  stimulated. 
To  overcome  the  errors  an  effort  of  the  accommodation  is  exerted, 
and  by  reason  of  the  differences  of  the  errors,  an  unequal  effort  of  the 
accommodation  is  demanded,  which  is  contrary  to  natural  law 
hence,  the  annoyances  of  which  the  person  complains.     The  effort 


144  OCULAR         R  K   F   R  A  C  T   I  O  X. 

accommodate  unequally  also  disturb  the  convergence,  creating  and 
adding  more  trouble. 

Asthenopia  may  be  expected  under  the  following  conditions  : 

First.      Hypermetropia  to  about  a  dioptre  or  less  in  both  eyes. 

Second.  Hyper  netropia  to  about  two  dioptres  or  less,  but  of 
unequal  amount  in  the  two  eyes. 

Third.  Emmetropia  in  one  eye,  ametropia  of  small  degree  in 
the  olher. 

Fourth.  Astigmatism  with  the  rule,  and  of  small  degree,  but  of 
unequal  amount  in  the  two  eyes. 

Fifth.     Astigmatism  in  one  eye,  none  in  the  other. 

Sixth.     Astigmatism  against  the  rule  and  of  very  small   amount. 

Seventh.  Those  cases  in  which  the  correction  required  is  a  con- 
tra-generic, sphero- cylinder,  the  extreme  of  difference  in  the  two 
principal  meridians  being  one  dioptre  or  less. 

It  should  be  remembered  that  a  small  amount  of  astigmatism 
against  the  rule  causes  more  trouble  than  a  far  greater  amount  with 
the  rule. 

Muscular  asthcEopia,  as  a  rule,  is  a  sequence  to  or  accompanies 
accommodative  asthenopia.  When  the  refractive  errors  are  correct- 
ed both  disappear. 


CHAPTER  VI. 

RETINOSCOPY. 

The  student  who  has  followed  the  studies  outlined  in  the  preced- 
ing chapter,  has  learned  the  conditions  required  for  normal  vision  ; 
also,  that  these  conditions  are  not  fulfilled  in  the  majority  of  cases, 
owing  to  errors  of  refraction. 

The  various  errors  that  occur  have  been  explained,  and  the 
character  of  the  lens  required  to  correct  each  has  been  shown,  so 
that  the  student  should  be  able  to  prescribe  the  lens  that  is  adapted 
to  any  given  condition,  provided  he  /oiows  what  tltc  condition  is. 

The  next  important  step  is  to  learn  by  ivliat  means  he  may  accur- 
ately determine  the  exact  conditions  of  refraction  as  they  exist  in  any 
eye. 

Various  methods  of  '' eye  testing'"  and  '•  eye  exa  initiation"  are 
used  to  ascertain  the  refraction  of  an  eye.  It  will  be  interesting  and 
instructive  to  devote  a  little  time  to  a  review  of  the  development  of 
the  art  of  adapting  lenses  for  the  eye. 

Not  many  years  ago  glasses  were  looked  upon  as  purely  a  com- 
mercial article,  to  be  purchased  from  the  stock  of  the  jeweler,  drug- 
gist, general-storekeeper,  or  even  the  street  peddler;  each  one 
claiming  superiority  for  his  special  brand  of  goods.  With  the  pur- 
chaser it  wasr.imply  a  question  of  trying  on  pair  after  pair  of  glasses 
until  he  found  one  through  which  he  could  see  with  the  most  satisfac- 
tion; he  merely  drew  comparisons  between  those  placed  before  him. 
This  method  differed  in  no  way  from  that  by  which  shoes  were  pur- 
chased by  the  same  person,  viz.,  try  on-fora-fit  (?). 

These  glasses  were  all  alike  in  two  respects  they  were  all  plain 
spherical  lenses,  that  were,  or  were  supposed  to  be,  alike  in  power 
for  each  eye. 

These  self- selected  glasses  were  not  always  satisfactory,  and  in 
many  instances  the  individual  found  himself  unable  to  obtain  any 
that  gave  him  relief. 

This  was  in  a  measure  due  to  the  fact  that  there  exists  in  most 
eyes  the  error  known  as  astigmatism,  which  requires  for  its  correction 
a  cylindrical  lens  Another  cause  of  dissatisfaction  with  the  stock 
glasses  was  that  they  failed  to  give  relief  when  there  was  a  difference 


146  OCULAR         REFRACTION 

in  the  refraction  of  the  two  associated  eyes,  and  many  of  us  are  now 
aware  that  this  condition  is  quite  common. 

These  conditions  served  to  bring  the  eye  specialist  into  existence. 
Professional  service  is  now  demanded;  people  will  no  longer  ''select" 
glasses,  but  wish  "advice"  as  to  what  they  should  have. 

If  the  eye  could  be  dismembered,  like  the  optical  instruments  of 
man's  construction,  and  the  various  parts  of  its  rcfractihg  system 
separately  considered,  the  art  of  prescribing  for  its  imperfections 
would  no  longer  be  a  difficult  one. 

This  is  impossible,  and  as  the  eye  possesses  that  wonderful  ad- 
justing and  compensating  power,  known  as  the  accommodation, which 
acts  involuntarily,  and  hides  more  or  less  the  errors,  the  art  of  esti- 
mating accurately  and  correcting  the  visual  defects  is  truly  a  delicate 
and  difficult  one. 

Just  how  reliable  the  various  methods  of  examination  are,  as 
practiced  by  the  oculist  and  optician,  many  have  reason  to  know. 
Each  specialist  arrives  at  a  different  conclusion  upon  the  completion 
of  his  examination  and  prescribes  lenses  accordingly.  If  the  case  is 
at  all  a  complicated  one,  two  prescriptions  will  rarely  be  similar;  wide 
differences  existing  between  the  powers  of  the  various  spherical  and 
cylindrical  lenses,  and  their  combinations,  while  there  is  often  a  dif- 
ference of  many  degrees  in  the  location  of  the  axis  of  the  supposedly 
correcting  cylinders. 

This  variance  of  opinion  is  either  due  to  lack  of  skill  upon  the 
part  of  the  specialist  or  faulty  methods  employed;  presumably  the 
latter,  for  who  can  correctly  say  just  how  much  or  what  he  sees  upon 
the  test  card  of  letters  after  having  dozens  of  lenses  placed  before  his 
eyes  in  rapid  succession  for  half  an  hour  or  more? 

This  form  of  examination  is  what  is  known  as  the  "  Su/'/ei/iiY 
Method"  because  the  information  the  specialist  acquires  is  obtained 
through  the  medium  of  the   individual  under  examination. 

The  precision  required  in  accurately  determining  the  condition  of 
the  eye's  refraction  should  not  alone  be  based  upon  the  answers  given 
by  the  patient,  but  primarily  upon  facts  obtained  by  the  specialist  from 
his  own  direct  observation  of  the  eye  itself. 

This  system  constitutes  the  "  dhjecthc  Method  " 

If  subjective  methods  alone  are  used  in  ocular  refraction,  there  can 
be  no  absolute  certainty  of  the  accuracy  of  the  correction.  The  rea- 
son for  this  is  that  by  subjective  tests  it  is  impossible  to  determine 
ra«.ff,  reasoning  from  (V/i'i/.  In  hypermetropia,  myopia,  or  in  astigma- 
tism, circles  of  diffusion  occur  upon  the  retina,  to  create  a  blurred 
image  and  reduce  the  visual  acuity.     The  proof  of  this  is    seen    in    the 


R  E  T  I  N  O  S  C  O  P  Y.  147 

mistakes  that  are  made,  myopia  being  diagnosed  when  hypermetropia 
exists;  hypermetropia  being  prescribed  for  when  astigmatism  is  the 
error,  etc. 

By  objective  examination  the  refraction  may  be  determined  by 
observation  of  the  operator,  and  he  may  thus  obtain  at  least  an  idea 
of  the  possibilities  of  vision  before  he  asks  anv  questions  of  the  patient. 
He  is  enabled  to  reason  from  cause,  Jirect  to  effects  that  he  can  observe. 

A  comparison  of  Subjective  Methods  with  Objective  Methods 
means  inaccuracy  compared  to  accuracy. 

"  Ours  is  an  age  of  progress."  Man  has  advanced  in  the  arts  of 
life;  he  has  advanced  in  knowledge. 

Within  the  past  ten  years  the  advance  in  the  science  of  adapting 
lenses  to  tiie  correction  of  errors  of  refraction  has  been  greater  than 
in  the  preceding  fifty.  It  has  been  largely  in  one  direction,  viz.: 
''Objective  Exaininatioii,"  which  is  scientific. 

"  Siil'jective  testing,'"  wh\c\\  \s  not  scientific,  has  not  kept  pace 
with  it,  nor  could  it  be  expected,  for  it  has  certain  limitations  that 
were  practically  reached  by  experts  in  that  method  years  ago. 

The  progress  in  Objective  Methods  has  led  to  greater  accuracy 
in  diagnose  and  given  greater  satisfaction  to  the  wearers  of  glasses. 
This  has  educated  the  public  to  a  keener  appreciation  of  the  value  of 
good  vision  and  visual  comfort,  and  a  consequent  greater  demand 
for  correctly  adapted  glasses. 

For  nearly  three-quarters  of  a  century  it  has  been  known  that 
under  certain  conditions  the  pupil  of  the  human  eye,  which  ordinar 
ily  appears  to  be  black,  can  be  made  to  appear  luminous,  somewhat 
like  the  glow  of  a  cat's  eye  in  the  dark. 

This  phenomena  seems  to  have  awakened  no  investigation  until 
about  1850,  when  Cniiuiiings  and  Bruccke  developed  suitable  means 
for  bringing  this  about  in  a  practical  manner. 

In  185 1,  Von  He/ni/toltrj  gSive  io  the  world  his  great  discovery, 
the  Ophthalnwscope,  which  served  to  revolutionize  the  science  of 
ophthalmology.  With  it  the  specialist  was  enabled  to  observe  the  in- 
terior of  the  eye  during  life,  by  illuminating  its  depths. 

Previous  to  the  invention  of  this  instrument  the  human  eye's  in- 
terior was  a  sealed  book  until  after  death. 

The  glowing  appearance  of  the  pupil,  observable  when  the  oph- 
thalmoscope is  used,  did  not  appear  to  excite  any  special  interest  for 
many  years  after  the  invention  of  this  instrument,  although  it  was 
early  noted  that  the  luminosity  of  the  pupil  varied  greatly  in  difTer- 
ent  eyes. 


148  OCULAR         REFRACTION. 

In  1873,  Cniguet  announced  that  this  difference  in  appearance 
was  directly  traceable  to  the  character  of  the  refraction  of  the  ob- 
served eye.  Parent  supplemented  Ciiignct's  work,  and  in  18S1  proved 
conclusively  that  the  refraction  of  the  eye  could  be  positively  deter- 
mined by  observing  the  character  of  the  retinal  reflex  as  manifested  in 
the  luminous  pupil. 

The  phenomena  of  the  luniinoics pupil  is  brought  about  by  send- 
ing a  beam  of  light  into  the  eye  by  reflection  from  a  small  mirror  hav- 
ing a  peephole  at  its  centre.  This  light  passes  through  the  refract- 
ing system  and  is  focused  upon  a  small  area  of  the  retina,  which  in 
turn  reflects  a  portion  of  the  light  back  through  the  peep-hole  in  the 
mirror  to  the  eye  of  the  observer,  who  is  thus  enabled  to  study  the 
character  of  the  retinal  reflex. 

Parent  gave  the  name  retinoseopy  to  this  scientific  method  of  ex- 
amination, and  the  instrument  he  devised  for  use  in  its  practice  he 
called  the  rctinoscope. 

Retinoseopy  is  endorsed  and  practised  by  all  the  leading  eye- 
specialists  of  the  world,  a  few  opinions  regarding  its  value  will  be 
quoted. 

Probably  one  of  the  greatest  living  authorities  upon  the  eye  is 
Dr.  M.  Tscherning,  who  succeeded  the  great /^rrv?/  as  director  of  the 
Laboratory  of  Ophthalmology  at  the  Sarbonne  in  Paris.      He  says  : 

"  I  have  several  times  emphasized  the  advantages  which  retinos- 
eopy with  a  luminous  point  presents  for  the  study  of  optic  anomalies 
of  ths  eye  It  also  lends  itself  very  well  to  the  ordinary  measure- 
ment of  refraction." 

The  most  prominent  English  authority.  Dr.  Gustavus  Hartridge, 
says  : 

"  Retinoseopy  is  deservedly  one  of  the  most  popular  methods  of 
estimating  refraction.  The  chief  advantage  is  that  it  is  entirely  ob- 
jective and  is  therefore  very  useful  in  the  cases  of  young  children,  in 
those  that  are  amblyopic,  and  in  maligners;  besides,  the  method  is 
quickly  carried  out,  saving  much  time  in  difficult  cases  of  astigma- 
tism. Retinoseopy  also  enables  us  to  easily  detect  small  degrees  of 
astigmatism,  which  frequently  exist,  and  but  for  this  method  would 
probably  escape  notice." 

In  thecorrection  of  visual  defects,  asin  many  other  achievements,, 
American  specialists  lead  the  world.  Probably  the  most  widely 
known  authority  upon  retinoseopy  is  Dr.  Janus  Tliorington,  of  Phila- 
delphia. His  writings  upon  the  subject  have  been  used  as  text-books 
and  translated  into  many  languages.     He  says  of  retinoseopy: 


R  E  T  I  N  O  S  C   O  P  Y.  149 

"With  an  eye  otherwise  normal,  except  for  its  optic  error,  and 
under  the  influence  of  a  reliable  cycloplegic,  there  is  no  more  exact 
objective  method  of  obtaining  its  refraction  than  by  retinoscopy.  Its 
advantages  are  that  the  character  of  the  refraction  is  quickly  diagnos- 
ed. The  refraction  is  estimated  without  the  verbal  assistance  of  the 
patient.  The  correction  is  quickly  obtained.  The  value  of  retinos- 
copy can  never  be  over-estimated  in  the  young,  in  the  feeble-minded, 
the  illiterate,  in  cases  of  nystagmus,  amblyopia  and  aphakia.  Of  all 
the  objective  methods  of  refraction,  retinoscopy  in  the  hands  of  the 
expert  is  the  most  exact." 

Retinoscopy  may  be  learned  theoretically  or  practically.  There 
are  many  Refractionists  who  are  good  practical  operators  with  the 
retinoscope  who  do  not  know  its  theory.  There  are  also  many  who 
understand  the  theory  and  yet  are  unable  to  put  it  into  practical  use. 
It  is  needless  to  say  that  theory  and  practical  application  should  be 
learned  together. 

Anyone  may  be  taught  in  a  few  moments  to  handle  the  retino- 
scope so  that  they  may  see  that  it  causes  the  pupil  to  appear  lumin- 
ous, but  it  conveys  no  meaning  to  their  untrained   mind. 

To  attain  proficiency  in  the  use  of  the  retinoscope  involves 
special  training  of  the  hand,  the  eye,  and  the  mind  of  the  Refraction- 
ist. 

The  /land  mnst  learn  to  control  the  instrument  so  as  to  project 
the  light  beam  from  it  into  the  observed  eye  in  various  ways,  ac;ord- 
ing  to  the  existing  conditions  that  may  be  indicated  to  the    observer. 

The  eve  of  the  observer  must  be  trained  to  recognize  and  differ- 
entiate between  the  various  appearances  of  the  retinal  reflex,  as 
manifested  in  the  luminous  pupil. 

The  mind  must  be  capable  of  quickly  interpreting  the  meaning 
of  the  observed  reflex,  and  dictating  the  procedure  to  estimate  the 
error  of  refraction  if  such  exists,  and  its  correction. 

In  order  to  have  a  clear  understanding  of  retinoscopy,  one  should 
understand  the  principles  upon  which  the  ophthalmoscope  is  con- 
structed and  operated,  because  the  retinoscope  is  constructed  upon 
the  same  principles,  and  used  in  the  same  manner,  up  to  a  certain 
point,  viz: — the  illumination  of  the  retina. 

In  chapter  I,  figures  8  and  9,  illustrate  two  conditions  under 
which  light  is  reflected.  Figure  8,  shows  that  lignt  rays  that  strike  a 
surface  perpendicularly  are  reflected  back  along  the  path  by  which 
they  approached;  the  paths  of  the  incident  and  reflected  rays  being 
the  same.     Figure  9,  shows    that    when    the    incident    ray    forms  an 


OCULAR 


R   K  F  K  A  C  T 


angle  wilh  the  perpendicular,  the  reflected  ray  forms  an  equal    angle 
with  the  perpendicular. 

In  the  use  of  the  ophthalmoscope,  the  conditions  shown  by  figure 
8  are  followed.  Light  is  reflected  through  the  pupil  to  the  retina, 
which  absorbs  a  portion  of  it,  but  a  portion  is  reflected  from  the  retina 
outward  through  the  pupil.  The  operator's  eye  is  so  placed  behind 
the  ophthalmoscope,  that  it  is  in  the  path  of  these  emergent  rays,  and 
receives  some  of  them.  The  pupil  of  the  observed  eye  no  longer 
appears  black  under  these  conditions,  but  is  illuminated. 


Incorporated  in  the  opr.thalmoscope  are  lenses  that  are 
bring  the  emergent  rays  to  a  focus,  so  that  the  observer  may 
study  the  pathologic  conditions  of   the  retina. 

The  retinoscope  is  simply  an  instrument  to  project  light  u 
retina;  it  carries  no  lenses  back  of  tne  peep  hole,  such  as  are 
the  ophthalmoscope. 


used  to 
see  and 


pon  the 
tised  in 


^ 


Figure  i  i6. 

Dr.  Thorington's  Retinoscope. 

It  consists  of  a  mirror  which    is    capable   of  refit  cting    the    light 
from  some  definite  source,  through  the  refracting  system  and  pupil  of 


R  E  T  I  N  O  S  C  O  P  Y.  151 

the  observed  eye,  so  that  a  portion  of  the  retina  becomes  an  illumin- 
ated body. 

To  simplify  the  subject  as  much  as  possible,  only  the  plane  mir- 
ror  rctinoscope  will  be  considered,  and  the  method  of  its  use  explain- 
ed.    The  concave  mirror  will  be  taken  up  later. 

Figures  J15  and  116,  will  illustrate  two  forms,  and  it  is  simply  a 
matter  of  personal  preference  to  select  either  the  large  or  the  small 
mirror;  either  will  do. 

The  light  source  has  always  been  a  perplexing  problem  in  retin- 
oscopy.  In  reading  over  numerous  articles  upon  the  subject,  the 
reader  will  be  surprised  at  the  differences  of  opinion  upon  this  point. 
All  kinds  and  conditions  of  light  are  advocated,  with  various  screens 
and  shades.  In  addition  to  this,  the  position  of  the  light  with  refer- 
ence to  the  patient  and  the  retinoscope,  is  the  subject  of  a  variety  of 
opinions.     This  only  serves  to  confuse  the  student. 

The  writer  will  no  doubt  cause  a  storm  of  criticism  when  he  states 
that  too  much  importance  is  attached  to  these  conditions. 

It  is  desirable  that  the  light  source  should  be  brilliant,  wiih  an 
even  area  of  illumination.  An  electric  lamp  of  the  incandescent  type, 
with  sanded  globe  is  quite  satisfactory.  One  of  sixteen  candle  power 
will  serve  for  most  cases,  or  if  more  light  is  required,  a  thirty-two 
candle  power  may  be  used.  If  electric  light  is  not  available,  a  Wels- 
back,  or  better  still,  a  Kern  type  of  incandescent  gas  burner  is 
e.xcellent. 

The  light  should  be  placed  behind  the  patient,  at  the  level  of  the 
eyes,  and  a  little  to  one  side;  either  side  will  be  correct. 

The  important  thing  to  do  is  to  have  the  light  so  placed,  that 
when  the  observer  takes  his  position  facing  his  patient,  as  shown  in 
plate  135,  he  may  be  able  to  project  the  light,  reflected  by  his 
retinoscope,  directly  into  the  eye  of  his  patient.  His  object  is  to  get 
the  light  into  the  eye  so  that  he  may  observe  the  emergent  rays. 

It  is  not  necessary  to  confuse  the  student  by  elaboration  of  the 
character  of  the  entering  rays,  that  may  be  taken  up  later;  it  is  only 
necessary  to  consider  that  they  enter  under  fixed  conditions,  with  the 
plane  mirror,  and  emerge  in  aeeordanee  ivith  the  refraetion  of  the  eye. 

It  is  known  that  objects  are  seen  by  the  light  that  they  send  to 
the  eye,  either  by  radiation  (luminous  bodies),  or  reflection  (illumin 
ated  bodies). 

If  the  retina  were  a  luminous  surface,  light  would  be  emitted 
from  the  eye,  and  the  pupil  would  present  a  luminous  appearance 
instead  of  appearing  black.       If  this  were  true,  and  the  emitted  light 


152  OCULAR         R   K  F  R  A  C  T   I  O  N. 

were  of  sufficient  intensity,  it  would  not  be  necessary  to  illuminate 
the  retina  by  projecting  light  upon  it,  and  the  retinoscope  would  have 
ito  be  constructed  upon  quite  a  different  plan. 

Not  being  a  luminous  surface,  it  is  necessary  to  make  the  retina 
an  illuminated  surface,  in  order  that  some  light  maybe  reflected  out- 
ward through  the  pupil. 

The  ophthalmoscope  and  the  retinoscope  are  both  used  to  illu- 
sminate  the  retina. 

In  the  use  of  the  ophthalmoscope,  the  operator  studies  the  appear- 


Figure   117. 

Directibn  of  emergent  rays  from  an  Emmetropic  eye  in  a  static  condition,  under  observation 
with  the  retinoscope.     Emergent  rays  parallel. 

ance  of  the  retina  and  its  component  parts  in  search  of  pathologic 
conditions.  The  refraction  of  the  eye  may  also  be  estimated  with  the 
ophthalmoscope. 

In  the  use  of  the  retinoscope  the  Ocular  Refractionist  studies  the 
character  of  the  emergent  rays  reflected  from  the  retina,  because  he 
knows  that  according  to  the  character  of  the  refracting  system  of  the 
eye,  and  its  relative  position  with  regard  to  the  retina,  the  emergent 
rays  take  different  directions. 

It  has  been  taught  that  the  emmetropic  eye,  in  a  static  condition, 
is  adapted  to  ioo.wi  parallel  rays  of  light  upon  its  retina,  because  the 
retina  is  situated  at  the  principal  focus  of  its  refracting  system.  See 
figures  95  and  102. 

If  light  be  reflected  from  the  retina  of  an  emmstropic  eye  in  a 
static  condition,  tlie  rays  loill  emerge  parallel.  See  figure  117,  the 
arrows  indicate  the  direction  of  the  rays. 


R  E  T  I  N  O  S  C  O  P  Y.  153 

The  hypermetropic  eye,  in  a  static  condition,  is  adapted  to  focus 
convergent  rays  to  a  focus  upon  its  retina,  because  the  principal  focus 
of  its  refracting  system  is  situated  at  a  point  behind  the  retina.  See 
figures  106  and  107.  If  light  be  reflected  from  the  retina  of  a  hyper- 
metropic eye  in  a  static  condition,  the  rays  zvill  eiufrge  divergent.  See 
figure  118.  The  degree  of  divergence  will  depend  upon  the  length 
of  the  antero  posterior  diameter.  The  nearer  the  retina  is  situated  to 
the  refracting  system  the  greater  will  be  the  divergence.  Another 
way  of  considering  the  condition  is;    that  of  two  hypermetropic  eyes, 


tion  with  the  relinoscope.      Emergent  rays  divergent. 

the  one  having  the  greater  error  of  refraction,  will  give  the  greater 
divergence  to  the  emergent  rays.  This  is  a  significant  pomt  to  get 
clearly  in  mind,  because  it  has  an  iinportant  bearing  upon  the  actual 
practice  of  retinoscopy,  as  will  be  demonstrated  later  on. 

The  myopic  eye  is  adapted  to  receive  and  focus  upon  its  retina, 
only  divergent  rays  of  light,  because  its  retina  is  situated  beyond  the 
principal  focus  of  its  refracting  system.     See  figures  109  and  no. 

Light  rays  reflected  from  the  retina  of  a  myopic  eye  liave  a  con 
vergence  as  they  emerge.     See  figure  119. 

The  degree  of  convergence  of  the  emergent  rays  is  dependent 
upon  the  axial  length  of  the  eye,  and  the  location  of  the  point  at 
which  these  rays  converge,  or  focus,  is  dependent  upon  the  same 
condition.  The  nearer  the  retina  is  situated  to  the  principal  focus, 
the  less  convergent  the  emergent  rays  will  be. 

The  focus  of  the  emergent  rays  from  a  myopic  eye  is  designated 


154 


O  C    U  L  A  R 


REFRACTION 


as  its  far  point  (P.  R. ).  Of  two  mj'opic  eyes,  that  in  which  the  higher 
myopia  exists,  the  nearer  will  its  far  point  be.  The  student  must  fix 
this  fact  clearly  in  mind  as  it  is  of  the  utmost  importance. 

In  the  astigmatic  eye,  owing  to  its  unequal  power  of  refraction  in 
various  meridians,  the  emergent  rays  take  different  directions. 


Figure  1.9. 

il^h, 

Irom  a  Myopic   eye,    under  observat 

on    with  the  retino- 

■ope. 

Emergent  rays  convergent. 

In  simple  hypermetropic  astigmatism,  the  rays  emerge  parallel  in 
one  meridian,  while  in  the  meridian  at  right  angles  to  it,  they  emerge 
divergent  In  compound  hypermetropic  astigmatism,  the  rays 
emerge  divergent  in  all  meridians,  but  more   so  in  some  ttian  others. 


Plan  of  bicvi 


of  emergent 

•ht 


The  meridians   of  greatest  and  least  divergence  are  always  at     ^ 
angles  to  each  other. 

_  In  simple   myopic  asticrmatism,  the  rays  emerge  parallel  in  one 
meridian,  while   in    the   meridian   at   right   aii^jles  to  it,  they  emerge 


R   E  T  I  N  O  S  C  O  r  Y.  155 

convergent.  If  the  eye  possesses  compound  myopic  astigmatism,  the 
rays  emerge  convergent  in  every  meridian,  but  more  so  in  some  than 
others.  The  meridians  in  which  the  greatest  and  least  convergence 
occurs  are  always  at  right  angles  to  each  other. 

The  emergent  rays  from  an  eye  that  possesses  mixed  astigma- 
tism, are  convergent  in  some  meridians,  divergent  in  others.  The 
meridian  in  which  the  greatest  ivergence  occurs  is  always  at  right 
angles  to  the  meridian  in  which  the  greatest  convergence  occurs. 
Figure  1 12  shows  how  parallel  rays  entering  an  eye  that  has  mixed 
astigmatism  are  brought  to  a  focus  in  its  two  principal  meridians. 
Th.e  emergent  rays  from  the  same  eye  would  diverge  in  the  vertical 
meridian,  and  converge  in  the  horizontal  meridian. 

In  order  to  make  as  clear  as  possible,  the  conditions  governing^ 
the  emergent  rays  of  light  from  the  eye,  the  principle  upon  which  a 
bicycle  lamp  is  constructed  will  be  explained,  and  the  emergent  rays 
from  such  a  lamp,  and  those  from  an  eye,  will  be  compared. 


Figure   121. 

Lighted  candle   paced  at  the    piiiicipal    focus   of  a  con' 


Let  figure  120  represent  the  plan  of  a  bicycle  lamp.  The  lens  is 
a  double  convex  spherical,  with  the  flame  of  the  lamp  situated  just 
inside  of  the  principal  focus;  this  gives  to  the  emergent  rays  only  a 
slight  divergence.  Behind  the  flame  is  placed  a  concave  mirror  that 
reflects  the  light  that  strikes  the  back  of  the  lamp,  forward  through 
the  lens.  The  nearer  the  light  is  placed  to  the  lens,  the  wider  diver- 
gence is  given  to  the  emerging  rays. 

Comparison  of  figure  120  with  figure  iis,  shows  that  the  emer- 
gent rays  from  the  bicycle  lamp,  and  those  from  a  hypermetropic  eye 
are  both  divergent;  therefore,  the  conditions  of  hypermetropia  are 
similar  to  those  of  the  lamp,  viz: — the  light  source  is  inside  the  prin- 
cipal focus  of  the  refracting  system. 


156 


OCULAR 


E  F  R  A  C  T  I  O  N. 


Another  comparison  may  be  drawn  between  this  lamp  and  the 
eye.  Looking  into  the  aperture  of  the  lens,  it  appears  black  until  the 
lamp  is  lighted,  when  it  appears  luminous.  Looking  into  the  aper- 
ture of  an  eye  it  looks  black  until  light  is  projected  upon  the  retina, 
which  reflects  a  portion  of  it  outward  through  the  pupil,  rendering  it 
luminous. 


Emergent  parallel  rays  brought 

At  this  point  the  student 


jure  122. 

focus  by  interposing  a  convex  spherical  lens, 
advised  to  refer  to  figures  3S,  39,  and 
4i,_  to  refresh  his  memory  upon  the   principles  they  illustrate;   viz: — 
principal  focus  and  conjugate  foci. 

According  to  the  laws  of  conjugate  foci,  the  following  experi- 
ments may  be  made. 

Let  figure  121  represent  a  convex  spherical  lens  of  eight  dioptres 
(+  8.00  D.  S.),  with  a  lighted  candle  placed  at  its  principal  focus, 
five  inches.  The  light  rays  strike  the  lens  divergent  and  emerge 
from  it  parallel.  If  it  is  desired  to  bring  these  parallel  emergent  rays 
to  a  focus  again  at  any  certain  distance  from  the  lens,  say  ten  inches, 
without    changing    the    relative    positions    of    the    candle    and    lens. 


Figure  123. 

A  lighted  candle   situated  at  a  point  inside  the  principal  focus  of  a   conve.x  spheiical  lens. 

Emergent  rays  divergent. 

it  will  only  be  necessary  to  place  a  convex  spherical  lens  of  the 
required  focal  length,  (+  4. 00  D.),  a  four  dioptre,  to  intercept  the 
rays  as  they  emerge  from  the  first  lens.  The  second  lens  will  cause 
them  to  converge  and  focus  ten  inches  away.     See  figure  122. 


R  E  T  I  N  O  S  C  O  P  Y. 


The  conditions  represented  by  figure  t2i  may  be  compared  to 
those  in  an  emmetropic  eye.  By  the  procedure  illustrated  by  figure 
172,  the  conditions  that  exist  in  a  myopic  eye  are  created. 


Figure  124. 

Diverging  emergent  rays  brought  to  a  focus  by  interposition  of  a  convex  spherical  lens. 

Let  figure  123  represent  a  convex  spherical  lens,  the  lighted  can- 
die  is  nearer  the  lens  than  its  principal  focus,  consequently  the  diverg- 
ing rays  that  strike  the  lens,  emerge  divergent.  In  order  to  render 
the  emergent  rays  parallel,  another  convex  lens  would  have  to  inter- 


Figure  125. 

Alighted  candle  placed  beyond  the  principal  focus  of  a  convex  spherical  lens,  emergent  rays 
convergent. 

cept  them.  If  it  should  be  required  to  bring  them  to  a  focus,  a  still 
more  powerful  convex  lens  would  have  to  be  interposed  between  the 
first  lens  and  the  point  at  which  it  is  desired  they  should  be  brought 
to  a  focus.      See  figure  124. 


Figure  126. 

Converging  emergent  rays  rendered  less   convergent  by  interposing  a  concave  spherical  lens. 

Figure  125  represents  the  candle  placed  beyond  the  principal 
focus  of  the  convex  lens,  the  emergent  rays  are  seen  to  converge 
as  they  emerge  from  the  lens. 


ISO  OCULAR         REFRACTION. 

Suppose  the  point  at  which  they  focus  is  eight  inches  from  the 
lens,  and  it  is  desired  that  they  should  focus  20  inches  away.  This  may 
be  broug-ht  about  by  interposing  a  concave  lens  of  the  proper  power 
( —  3.00  D.)  to  lessen  their  convergrence,  so  that  they  will  focus  at  the 
required  point.  See  figure  t26  The  dotted  lines  in  figures  126,  124 
and  122,  indicate  the  direction  the  emergent  rays  would  have  taken 
had  the  second  lenses  not  been  interposed. 

Compare  the  conditions  illustrated  by  figures  117  and  121  to  see 
that  they  are  alike.  The  same  is  true  of  the  conditions  illustrated  by 
figures  118  and  123  ;  also,  figures  1 19  and  125. 

A  study  of  the  optical  conditions  illustrated  by  the  figures  from 
117  to  126  inclusive,  reveals  that  through  the  aid  of  the  retinoscope  it 
is  possible  to  calculate  the  conjugate  foci  of  the  eye,  making  use  of  a 
lens,  or  combination  of  lenses,  oi  known  dioptric  value. 

From  these  knou'ii  lenses,  as  a  basis  for  calculation,  the  unknown 
dioptric  value  (conditions  of  refraction)  of  the  eye  under  observation 
may  be  determined  with  more  or  less  accuracy. 


I 


Figure  127. 
Conjugate  foci.     A,  luminous  point 

When  the  actual  diopf  c  conditions  of  the  eye  are  thus  made 
known,  its  errors  of  refraction,  if  any  exist,  may  be  corrected  with 
accurately  adapted  lenses. 

In  the  practice  of  retinoscopy,  the  Ocular  Refractionist  really 
learns  the  character  of  the  retinal  image,  when  observed  through  the 
medium  of  the  retinoscope  at  any  given  working  distance,  which 
is  erect  or  inverted  according  to  the  refraction  of  the  eye 

This  phase  of  the  subject  may  be  ignored  by  the  stndent  at  this 
time,  as  it  may  be  confusing,  it  is  merely  mentioned  so  that  the  writer 
may  not  be  accused  of  teaching  false  doctrines. 

Only  the  effects  of  light  and  shadow  movement  in  the  luminous 
pupil  created  by  the  use  of  the  retinoscope  need  be  studied  at  first. 

To  bring  up  the  subject  of  conjugate  foci  at  this  point  will  be 
advisable  to  illustrate  a  vital  point. 


R  E  T  I  N  O  S  C  O  r  Y.  ,59 

It  is  known  that  light  that  is  sent  to  a  convex  spherical  lens  from 
a  luminous  point,  so  that  the  rays  enter  the  lens  divergent  and  emerge 
convergent,  that  they  focus  at  another  point.  The  luminous  point 
and  the  focal  point  are  termed  conjugate  foci,  and  their  locations  are 
interchangeable. 

Let  figure  127  illustrate  this  proposition.  A,  is  the  luminous 
point;  B,  the  focal  point  on  the  opposite  side  of  the  convex  spherical 
lens.  If  the  luminous  point  be  moved  to  B,  the  focal  point  will  be 
located  at  the  position  A. 

In  the  calculation  of  conjugate  foci,  it  will  be  seen  that  it  is 
necessary  that  the  rays  should  converge  as  they  emerge  from  the 
lens.  The  author  has  coined  a  term  to  designate  these  conditions, 
viz  : — posit ii'c  conjugate  foci. 

In  explanation  of  this  term  it  may  be  stated  that  it  is  customary 
to  consider  that  a  convex  spherical  lens  has  a.  positii'c  focus,  see  figure 
38,  while  a  concave  spherical  lens  has  a  virtual  focus,  see  figure  54. 

Reference  to  figures  117,  118  and  119,  shows  that  only  the  rays 
from  a  myopic  eye  emerge  convergent,  therefore,  the  myopic  eye  has 
positive  conjugate  foci.  Those  from  the  hypermetropic  eye  emerge 
divergent,  and  from  the  emmetropic  eye  parallel;  hypermetropic 
and  emmetropic  eyes  have  virtual  conjugate  foci 

By  referring  to  figures  112  and  124,  it  will  be  seen  that  by  inter- 
posing convex  spherical  lenses,  positive  conjugate  foci  inay  be  created. 

In  the  practice  of  refinoscopy,  the  Ocular  Refractionist  locates  the 
viyopic  far  point  of  the  eye. 

If  the  eye  is  myopic  this  may  be  done  without  interposing  any 
lenses  whatever.  If  the  eye  is  not  myopic,  the  myopic  condition  may 
be  created  by  interposing  the  necessary  lens  or  lenses,  to  locate  the 
artificial  far  point  at  a  definite  distance. 

TJiis  definite  distance  from  the  eye  under  observation,  ivhich  the 
operator  selects,  is  called  the  working  distance. 

The  proper  working  distance  in  retinoscopy  has  been  the  subject 
of  much  discussion  and  diversitv  of  opinion,  which  tends  to  confuse 
the  student.  If  the  meaning  of  the  term  is  thoroughly  understood  it 
need  not  be  perplexing. 

In  the  majority  of  cases  it  will  be  found  that  a  working  distance 
of  forty  inches,  which  is  equal  to  one  metre,  will  be  most  convenient 
It  will  simplify  the  matter  of  making  allowance  for  the  working  dis- 
tance because  forty  inches  is  equal  to  the  focus  of  a  one  dioptre  lens. 
It  is  conveniently  near  to  the  patient,  so  that  lenses  may  be  chang- 
ed in  the  trial  frame    by  the  operator  without   leaving  his  position. 


OCULAR 


A   C  T   I  O  N. 


Figure 


It  is  sufficiently  far  away  to  enable    the   operator  to  note   the  slight- 
changes  in  the  appearance  of  the  reflex  as  the  reversal  point  is  neared. 


R  E  T  I  N  O  S  C  O  P  Y.  I6i 

If  the  pupil  is  small,  as  frequently  occurs  with  elderly  people;  or 
the  reflex  is  dull  and  indistinct,  which  may  be  due  to  a  high  degree  of 
error  of  refraction  or  a  dense  retinal  pigment,  a  nearer  point  than 
forty  inches  may  have  to  be  selected,  for  the  working  distance. 

These  points  will  be  more  fully  explained  in  describing  actual 
practice. 

Fortunately  the  introduction  of  the  luminous  retinoscope,  see 
figure  1 28,  carrying  its  own  source  of  light,  simplifies  the  working 
conditions  and  affords  the  refractionist  ample  freedom  to  choose  any 
working  distance  best  suited  to  the  case  in  hand.  The  position  of 
the  light  source  may  be  ignored  because  it  is  always  under  control. 
The  intensity  of  the  light  may  be  regulated,  and  increased  to  such 
brilliancy  that  a  reflex  may  be  obtained  under  all  conditions. 

It  is  hoped  that  the  author  has  made  it  sufficiently  clear  that  any 
distance  may  be  selected  as  the  working  distance;  but  conditions  are 
imposed  that  bring  the  location  of  the  working  distance  within  cer- 
tain well  defined  limits.     This  knowledge  will  come  with  practice. 


Figure  129. 

An  emmetropic  eye  under  observation  with  plane  mirror  retinoscope,   working   distance   one 

metre.     O.   eye   of  observer;   M,  retinoscope;    E,  eye  under  examination.     The  unbroken 

''^es  represent  entering  parallel  rays;  the  dotted  lines  represent  the  emergent  rays,    also 

parallel. 

An  earnest  endeavor  has  also  been  made  to  ma"ke  the  subject  of 
conjugate  foci  as  clear  as  possible,  and  the  student  is  urged  not  to 
pass  beyond  this  point  until  he  has  the  matter  clearly  in  mind.  The 
importance  of  this  cannot  be  overestimated,  because  the  theory  and 
practice  of  retinoscopy  is  founded  upon  the  physical  laws  governing: 
conjugate  foci. 

Let  figure  129  represent  an  eye,  E,  under  examination  with  a 
plane  retinoscope  M;  the  position  of  the  operator  is  one  metre,  or 
forty  inches  distant;  his  eye  is  represented  by  O  which  is  behind   the 


O  C   U  L  A  R 


REFRACTION 


retinoscope.  Figure  129  represents  the  conditions  that  occur  if  the 
eye  E  be  emmetropic.  The  parallel  rays  represented  by  the  un- 
broken lines,  are  seen  to  be  reflscted  from  the  plane  mirror  M,  into 
the  eye  E.  As  the  eye  is  emmetropic  the  rays  that  are  reflected  from 
its  retina  emerge  parallel,  and  some  of  them,  represented  by  the  dot- 
ted lines,  reach  the  eye  O  of  the  observer  as  parallel,  through  the 
peep-hole  in  the  mirror. 


Figure   130. 

Emergent  rays  Irom  an  emmetropic  eye  brought  to  a  focus  i 
metre,  by  a  convex  spherical  lens  of  one  dioptre. 

Suppose  it  is  desired  to  converge  the  emergent  parallel  rays 
shown  in  figure  129,  so  they  will  focus  at  the  position  of  the  observer 
40  inches  distant. 

As  it  is  known  that  a  convex  spherical  lens  of  one  dioptre  will 
bring  parallel  rays  to  a  focus  at  forty  inches,  if  such  a  lens  be  placed 


Emergent   rays  from  an  eye,   myopic 
distance  of  one  metre,  by  ; 

before  this  emmetropic  eye,  as  illustrated  by  figure  130,  the  emergent 
rays  will  focus  at  the  observer's  eye  O.  The  dotted  lines  represent 
the  emergent  rays,  and  show  that  their  direction  is  changed  from 
parallel  to  convergent  by  the  one  dioptre  convex  lens  interposed. 

If  the  eye  under  observation,  shown  in  figure  130  were  myopic  to 


R  E  T  I  N  O  S  C  O  P  V. 


163 


one  dioptre,  the  emergent  rays  would  focus  at  the]observer's  eye  at 
forty  inches  distance  without  interposing  any  lens. 

Let  figure  131  represent  an  eye  that  is  myopic  to  four  dioptres, 
the  emergent  rays  woull  focus  at  a  distance  of  ten  inches,  its  far 
point.  If  the  observer  with  the  retinoscope  were  forty  inches  away, 
in  order  to  bring  them  to  a  focus  at  this  position,  it  would  be  necessary 
to  impose  a  concave  spherical  lens  of  three  dioptres.  This  lens  is 
seen  to  render  the  em  jrgent  rays  less  convergent,  as  shown  by  the 
dotted  lines,  figure  131.  The  conditions  are  now  similar  to  those 
shown  in  figure   130. 

Figure  132  represents  an  eye  that  is  hypermetropic  to  two  di- 
optres, under  observation  with  a  plane  retinoscope,  the  observer 
being  again  one  metre  distant.     The  emergent  rays  are  divergent  but 


Emergent  rays  fro:n  an  ey;,  hyp;r,n;trj,5 
ing  distance  of  01;  m;tre,  by  : 


to  two   dioptrei,    bro  ight  to  a  focus  at  the  work- 
:ja/ex  spherical  lens  of  three  dioptres. 


by  interposmg  a  con  vex  spherical  lens  of.  three  dioptres  they  are  con- 
verged and  focussed  at  the  observer's  eye.  These  conditions  are  now 
similar  to  those  shown  in  figure  130.  The  direction  of  the  emergent 
rays,  indicated  by  the  dotted  lines,  is  changed  by  the  convex  lens. 

It  will  be  seen,  from  the  foregoing,  that  in  the  practice  of  retin- 
oscopy,  if  the  eye  under  examination  be  myopic  to  one  dioptre,  or 
more,  that  its  far  point  may  be  determined  with  the  retinoscope.  If 
it  is  not  myopic,  by  imposing  certain  required  lenses,  a  myopic  con- 
dition may  bs  created  for  the  emergent  rays  aad  the  location  of  the 
far  point  determined. 

In  explanation  of  the  above,  a  simple  analogy  may  be  drawn. 
Suppose  one  has  a  quantity  of  small  blocks,  exactly  an  inch  square 
and  one-eighth  of  an  inch  in  thickness,  and  it  is  desired  to  place  them 
in  piles  of  twenty-four  each,  making  the  height  of  each  pile  three 
inches.  The  simplest  way  to  do  this  would  be  to  count  out  twenty- 
four   and    stack  them    into  one  pile,  as  a  measure,  see  A,  figure  133. 


1 64 


OCULAR 


REFRACTION 


The  pile  B  is  too  short,  and  the  pile  C  too  tall,  as  the  dotted  line 
shows.     Some  must  be  taken  from  C,  and  more  added  to  B. 

If  someone  should  ask  the  height  of  the  piles  B  and  C  as  they 
were  originally,  and  say  that  the  blocks  in  each  must  not  be  counted, 
nor  the  piles  measured,  the  problem  could  be  solved  by  counting  the 
number  it  was  necessary  to  add  to  B,  and  the  number  it  was  required 
to  take  from  C.  These,  compared  to  the  known  quantity  in  A,  will 
serve  as  a  basis  from  which  to  calculate  the  numbers  in  B  and  C,  and 
the  height  of  the  two  original  piles. 

Thus,  in  the  practice  of  retinoscopy,  if  a  certain  lens  value  is  re- 
quired to  be  imposed  to  focus  emergent  rays  to  a  definite  point,  one 
may  calculate  the  unknown  refraction  of  the  eye. 


Figure  133. 

Diagram  to  represent  the  meaning  of  the  term,  "  Working  distance  in  retinoscopy." 

These  propositions  will  no  doubt  seem  simple  enough  to  the  stu- 
dent, the  bringing  to  a  focus  of  the  emergent  rays  to  a  definite  point, 
by  the  interposing  of  certain  lenses  under  certain  conditions;  but,  he 
may,  and  doubtless  will  ask— How  is  one  to  know,  when  one  observes 
an  eye  with  the  retinoscope,  whether  it  is  emmetropic,  myopic  or 
hypermetropic? — The  answer  is;  the  appearance  of  the  luminous 
pupil  varies  according  to  the  diflterent  conditions  of   refraction. 

Thus  far  the  theory  of  retinoscopy  has  been  explained,  the  next 
step  will  be  to  take  up  acliial practice  and  -n'orking  conditions 

The  study  of  retinoscopy  has  brought  into  use  a  simple  device 
called  the  model  eye,  which  is  a  most  valuable  aid  to  the  student,  who 


RETINOSCOTY. 


165 


may  practice  upon  it  by  the  hour  without  its  entering  any  protest  of 
fatigue.  A  description  of  it  in  the  inventor's  own  words  will  suffice. 
It  is  shown  in  figure  134. 

"The  eye  is  made  of  two  cylinders  of  cardboard,  one  slightly 
smaller  than  its  fellow,  to  permit  slipping  easily  into  the  other.  Both 
cylinders  are  well  blackened  inside.  The  smaller  cylinder  is  closed 
at  one  end,  and  on   its   inner  surface  is  placed  a  colored  lithograph  of 


Figure  134. 

Model  eye  for  the  study  of  retinoscopy. 

the  normal  eye  ground.  The  larger  cylinder  is  also  closed  at  one 
end,  e.xcept  for  a  central  round  opening,  ten  millimeters  in  diameter, 
which  is  occupied  by  a  plus  twenty  dioptre  lens." 

"  On  the  side  of  the  small  cylinder  is  an  inde.x  which  records 
emmetropia,  and  the  amount  of  myopia  and  hypermetropia  according 
as  it  is  pushed  into  or  drawn  out  of  the  large  cylinder." 

In  other  words,  the  model  eye  can  be  "set  "  to  represent  emme- 
tropia, myopia  to  six  diopters  or  less,  and  hypermetropia  to  six 
diopters  or  less;  by  merely  sliding  the  two  cylinders  so  as  to  change 
the  axial  length  of  the  eye.  By  placing  a  cylinder  lens  from  the  test 
case  before  the  model  eye,  an  astigmatic  condition  may  be  created 
and  studied. 

These  cardboard  model  eyes  are  inexpensive  and  the  student  is 
advised  to  procure  four  of  them  for  the  purpose  of  practice.  Nearly 
all  knowledge  is  drawn  from  comparisons,  and  in  the  study  of  retin- 
oscopy the  opportunity  to  compare  effects  with  the  model  eyes  set  to 
represent  different  conditions  of  ametropia,  affords  valuable  practice. 

The  author  wishes  to  impress  upon  the  student  one  most  im- 
portant point  In  the  practice  of  retinoscopy  learn  to  be  inetliodical, 
for  it  is  a  scientific  test  that  is  based  upon  well  defined  laws,    and    to 


I66  OCULAR         REFRACTION. 

obtain  the  best  results  it  cannot  be  accomplished  with  careless 
methods.  Attention  7n?tst  be  given  to  details  of  position  of  tlic  patient, 
operator  and  tlie  light.  See  that  lenses  are  clean  and  properly  set  in 
trial  frame,  ichuh  niiist  be  set  to  the  proper  inter-pupillary  distance. 
Other  details  will  be  explained  in  their  proper  place. 

Retinoscopy  is  often  condemned  by  those  who,  through  their 
own  careless  practices,  are  unable  to  acquire  proficiency. 

To  '' make  haste  slowly  "  is  also  good  advice.  Retinoscopy  can- 
not be  learned  in  a  few  days,  nor  a  few  weeks.  This  statement  is 
not  intended  to  discourage  the  student,  nor  should  it  dampen  his 
ardor.  One  may  learn  in  a  ve?y  short  time  to  recognise  the  different 
errors  of 'refraction,  but  the  little  niceties  of  operating  the  instru- 
ment are  acquired  vi\th  practice.  All  cases  of  myopia  present  similar 
phases,  so  do  all  cases  of  hypermetropia;  astigmatism  of  like  char- 
acter shows  ^similarity  in  all  instances;  but  no  two  eyes  present 
exactly  the  same  appearance  under  the  retinoscope.  Differences  in 
the  size  of  the  pupils;  differences  in  the  density  of  the  retinal  pig- 
ment; differences  in  the  aberration  of  the  refracting  systems;  vary- 
ing effects  of  the  accommodation,  all  act  to  change  the  appearance  of 
the  retinal  refle.x. 

To  overcome  these  difficulties  one  must  have  practice.  The  old 
saying — "  Practice  makes  perfect" — certainly  applies  to  retinoscopy, 
only  it  may  be  modified  to — Practice  leads  to  proficiency;  therefore, 
take  the  model  eyes  and  practice,  practice,  practice. 

It  may  be  well  to  mention  that  if  the  refiactionist  has  an  error  of 
refraction  in  his  own  eye,  so  that  his  own  visual  acuity  is  impaired, 
he  should  wear  his  correction  in  using  the  retinoscope,  otherwise  he 
may  fail  to  recognize  what  he  sees.  The  wearing  of  one's  correction 
may  prove  annoying  to  some  extent,  owing  to  the  reflections  that 
occur  on  the  sui  faces  ©f  the  lenses,  but  a  little  experience  will  enable 
the  operator  to  overcome  this.  The  above  does  not  mean  that  the 
accommodation  of  the  operator  must  be  taken  into  consideration,  as 
in  the  use  of  the  ophthalmoscope,  but  merely  that  the  best  possible 
visual  acuity  is  essential  to  the  Refractionist  so  that  he  may  be  able 
to  recognize  what  he  sees. 

In  the  practice  of  retinoscopy  some  operators  advocate  the  use  of 
a  cycloplegic,  and  contend  that  the  test  is  useless  without  it.  The 
author  disputes  this  claim,  and  contends  that  not  only  is  a  cycloplegic 
not  necessary,  but  that  more  satisfactory  results  are  obtained  without 
it.  While  a  cycloplegic  holds  the  accommodation  in  abeyance,  it  di- 
lates the  pupil,  exposes  the  peripheral  portions  of  the  crystalline  lens 


R  E  T  I  N  O  S  C  O  P  Y.  i67 

and  discloses  its  aberrations  that  are  concealed,  or  cut  out  by  the  iris, 
under  normal  conditions.  The  accommodation  may  be  held  in  check 
by  other  means.  This  is  a  fortunate  circumstance  tor  the  optician, 
who  is  not  qualified  nor  permitted  to  use  a  cycloplegic.  It  also  meets 
with  the  approval  of  the  majority  of  people  who  object  to  "  drops  in 
the  eye." 


Workinc  toncl 


Plate    135 

inoscope  at  one  metre  di: 


positions  of 


168  OCULAR         REFRACTION. 

If  the  test  be  conducted  in  a  darkened  room,  the  pupil  will  dilate 
sufficiently  to  obtain  a  good  reflex.  The  refracting  room  need  not  be 
in  absolute  darkness,  particularly  if  using  the  self-luminous  retino- 
scope.  The  author's  refracting  room  is  painted  a  dull-surface  black, 
but  the  partition  does  not  extend  clear  to  the  ceiling,  so  that  a  suf- 
fused light  fills  the  room  which  is  only  comparatively  dark. 

The  only  direct  source  of  light  in  the  room  during  the  retinosco- 
pic  test  must  be  that  used  in  connection  with  the  instrument. 

PUtes  135  and  1  j6  are  made  from  photographs  taken  in  the 
author's  operating  rooms;  a  photograph  faithfully  reproduces  every 
detail,  and  these  plates  will  serve  better  than  any  diagram  to  illus- 
trate actual  working  conditions. 

The  patient  is  seated  in  a  revolving  chair,  which  permits  of  the 
proper  adjustment  for  height,  so  tliat  the  eyes  of  tlie patient  and  opera- 
tor are  on  a  level  ivitli  eacli  other. 

In  plate  135,  the  patient  and  operator  are  shown  one  metre 
apart.  The  allowance  for  working  distance  will  therefore  be  one 
dioptre. 

Patient  and  operator  face  each  other  sqitarely.  the  patient  directing 
his  look  fust  over  the  top  of  the  operator's  head  and  at  some  object  as  far 
away  as  possible. 

The  method  of  holding  the  retinoscope  is  plainly  seen,  the  instru- 
ment being  close  to  the  right  eye  of  the  observer.  The  instrument 
used  in  this  instance  is  a  luminous  one;  the  beam  of  light  is  seen  pro- 
jected from  the  retinoscope  into  the  left  eye  of  the  patient.  To  the 
patient's  right,  and  just  above  his  head,  will  be  seen  a  black  sheet 
iron  cylinder  attached  to  the  partition;  it  contains  a  sanded  electric 
lamp  which  emits  a  steady  light  through  the  circular  opening  in  the 
cylinder.  This  light  is  used  with  the  forms  of  retinoscope  illustrated 
by  figures  1 15  and  1 16.  This  sheet  iron  cylinder  makes  a  very  satis- 
factory screen  for  the  lamp,  the  top  an  bottom  being  closed.  Any 
tinsmith  will  be  able  to  make  one  at  a  small  cost. 

This  same  light  may  also  be  used  with  the  ophthalmoscope. 

To  control  the  beam  of  light  prof ected  from  the  retinoscope  requires 
considerable  practice.  It  may  be  supposed  that  it  is  a  simple  thing  to 
direct  the  mirror  so  that  the  light  will  reach  the  eye  of  the  patient. 
The  student  need  not  be  surprised  to  find  that  it  is  quite  difficult  at 
first;  in  fact,  that  he  cannot  locate  the  eye  with  it.  To  avoid  any 
such  evidence  of  lack  of  skill,  the  studsnt  should  not  attempt  the 
human  eye  until  he  has  had  some  practice  on  the  model  eyes.  A 
good  scheme  for  practice  will  be  to  paste  a  small  bit  of  paper,    about 


an  inch  in  diamer,  on  the  wall  at  the  level  of  the  eye  and  try  to  locate 
it  by  projecting  the  light  beam  upon  it. 

The  expression  — "  to  rotate  the  mirror  " — that  is    so    frequently 
used  in  describing  the  handling  of  the  instrument  is  apt  to  be  mislead- 


The  retinoscopic  exa 


ing;  while  it  is  entirely  correct,  it  may  make  the  point  clearer  to  state 
that  the  mirror  should  be  tilted  or  inclined. 

Plate  137  illustrates  the   correct  method    of    holding  the    retino- 
scope.     The  handle  is  lightly  but  firmly  grasped,  close  up  to  the  mir- 


I70 


OCULAR         REFRACTION. 


ror  ;  the  instrument  is  held'squarely  before  the  eye  and  touching  the 
forehead.     Either  eye  may  be  used  as  preferred  by  the  operator. 

The  mirror  is  inclined  in  various  directions,  or  tilted,  by  a 
movement  of  the  wrist  alone,  the  head  to  be  held  motionless.  This 
directs  the  movement  of  the  light  beam;  a  very  slight  movement  is 
sufficient  to  cause  the  light  to  pass  across  the  face  of  the  patient. 


Plate  137. 

Correct  method  of  holding  the  retinoscope. 

Some  operators  have  a  habit  of  holding  the  retinoscope  firmly 
against  their  forehead,  and  tilt  the  mirror  by  a  movement  of  the 
head,  to  the  right  and  left,  up  and  down,  etc.  This  style  of  operat- 
ing appears  awkward,  the  operator  bobbing  his  head  in  an  apparent- 
ly aimless  fashion;  it  gives  one  the  appearance  of  one  of  the  porce- 
lain figures  representing  a  Chinese  Mandarin. 


I 


R  E  T  I  N  O  S  C  O  P  Y. 


171 


It  is  just  as  well  to  cultivate  a  "clean-cut  style"  of  operating, 
which  is  not  difficult  ;  it  pays  well,  because  it  inspires  confidence  in 
the  patient  to  have  the  Refractionist  display  an  easy  manner  in  his 
work,  denoting  familiarity  with  it,  and  skill. 

Plate  138  illustrates  the  light  beam  from  the  retinoscope  project- 
ed directly  upon  the  eye.  In  the  illustration  it  is  seen  to  create  a 
circular  spot  of  light  upon  the  face,  about  two  inches  in  diameter. 

This  is  called  the  ''Light  Area." 

If  the  retinoscope  be  tilted  slightly,  this  light  area  will  of  course 
move  also,  and  a/:c,n's  in  the  Sd///e  direct  ion  as  the  mirror  is  tilted. 


Pla'e  138. 

Light  !)eam  from  the  retinoscope  directed  full  upon  the  ey 
area"  upon  the  face,  and  the  luminosity  of  the  pupil,  or  " 
in  contrast  with  the  darkness  in  the  pupil  of  the  other  eye 
photograph  from  life.  The  reflex  is  seen  occupying  the 
serves  to  illustrate  the  '  choked  "  appearance  of  the  refle 
located  with  the  retinosc 


ider  observation.     The   ''light 

inal  reflex,'    is  clearly    shown 

;.       This   plate    was  made   from  a 

entire   pupillary   area.       This  also 

X  when  the  "  point  of  reversal  "    is 


If  the  light  area  is  made  to  pass  across  the  pupil,  folloiving  a 
straight  line,  it  is  said  to  liave  made  a  ''transit  of  the  pupil." 

A  transit  of  the  light  area  thus  means,  that  in  passing  across   the 

pupil,  one  of  the  meridians  of  the  eye  is  followed.     By  means   of    the 

transit  of  the  light,  the  observer  is  enabled  to  estimate  the   character 

of  the  refraction  of  the  eye  in  that  one  particular  meridian  traversed. 

If  the  eye  be  emmetropic,  hypermetropic  or  myopic,  it  possesses 


172  OCULAR         REFRACTION. 

equal  refraction  in  every  meridian  ;  therefore,  in  determining  the  re- 
fraction in  one  meridian,  the  refraction  of  the  eye  is  obtained. 

Plate  138  shows  the  pupil  of  the  eye  under  observation,  located 
at  the  centre  of  the  light  area;  which  will  be  the  case  when  the  light 
beam  from  the  retinoscope  is  directed  full  upon  it.  The  pupil  is 
seen  to  be  illuminated,  the  contrast  between  it  and  the  darkness  of 
the  pupil  of  the  other  eye  being  quite  marked.  The  area  of  light  in 
the  pupil  is  brighter  than  the  light  area  upon  the  face,  so  that  it  is 
not  difficult  to  see  it. 

Under  these  conditions  the  pupil  is  said  to  be  "  hiniiiions."  It  is 
created  by  some  of  the  light  from  the  retinoscope  entering  the  eye 
through  the  pupil,  and  then  reflected  outward  by  the  retina  through 
the  pupil  again. 

The  light  seen  in  tJtc  hnninoiis  pjipil  is  called  the  "retinal   reflex." 

The  light  from  the  retinoscope  in  passing  through  the  refracting 
system  of  the  eye  is  focused  upon  a  comparatively  small  area  of  the 
retina.  Around  this  illuminated  spot  the  retina  is  in  darkness,  the 
areas  of  light  and  darkness  being  clearly  defined  and  in  contact  with 
each  other  This  may  be  demonstrated  by  focussing  light  with  a 
strong  convex  spherical  lens  upon  a  dark  surface. 

Looking  at  plate  13S  again,  and  noiing  that  the  pupil  of  the  eye 
under  examination  is  luminous,  while  the  pupil  of  the  other  eye 
appears  in  darkness;  it  is  obvious  that  ihe  reflex  is  created  by  the 
retinoscope,  and  if  the  light  area  is  passed  off  t/ie  pupil,  it  will  again 
appear  in  darkness  the  same  as  the  other. 

If  this  is  done,  the  light  area  being  made  to  pass  off  the  pupil 
slowly,  if  the  eye  possesses  spherical  ametropia,  that  is,  myopia  or 
hypermetropia,  the  retinal  reflex  does  not  disappear  instantly  from 
the  pupil  but  moves  off  slowly.  It  is  followed  by  an  area  of  shadow, 
so  that  an  area  of  light  and  shadow  is  seen  in  the  pupil  at  the  same 
time.     See  plates  139,  141,  142  and  143. 

This  area  of  light  and  shadow  in  the  pupil  is  merely  the  reflex  of 
the  light  area  surrounded  by  darkness  that  is  created  upon  the  retina. 

The  form  in  zvhich  the  lig/it  reflex  Joins  the  shadoi^',  denotes  the 
character  of  the  refraction  of  the  eye. 

If  the  shadow  sho7i's  a  crescent  shape  edge  adjoining  the  light,  it 
indicates  spherical  ametropia,  viz: — myopia  or  hypermetropia. 

Plate  139  represents  hypermetropia  or  myopia  as  indicated  by  the 
retinoscope.  The  method  of  determining  which  of  the  two  exists  in 
each  case,  will  be  explained  a  little  later  on.  In  plate  139  the  reflex 
is  seen  to  shade  off  gradually  into  the  shadow,  the  line  of  separation 


( 


R  E  T  I  N  O  S  C  O  P  Y.  173 

being  crescent  in  form.      The   form  of  the  crescent  varies  with   the 
degree  of  the  error. 

Plate  140  shows  an  entirely  different  appearance  of  the  reflex 
and  shadow  in  the  pupil,  the  line  separating  the  two  being  straight, 
the  reflex  assuming  the  appearance  of  a  bright  band  of  light  across 
the  area  of  darkness. 


Plate  139. 

Spherical  ametropia  as  indicated  by  the  retinoscope.  ""  The  light  area  in  the  pupil  shades 
gradually  into  its  following  shadow.     The  line  of  demarkation  being  of  crescent  form. 


Tills  light  band  is  typical  of  astigmatism,  zvhich  is  thus  indicated 
by  the  retinoscope. 

The  breadth  of  the  light  band,  the  definition  of  its  edges,  and  its 
brilliancy,  varies  with  the  degree  of  the  error. 

The  direction  of  the  light  band  indicates  the  location  of  the  axis  of 
the  cylindrical  lens  required  to  correct  the  error. 

The  direction  of  the  light  band  thus  indicates  one  of  the  principal 
meridians  of  the  refracting  system  of  the  eye,  the  other  principal 
meridian  is  always  at  right  angles  to  the  light  band.  The  value  of 
the  retinoscope  will  thus  be  seen,  in  not  only  detecting  astigmatism, 
but  also  in  locating  the  axis  of  the  correcting  cylinder. 


174  OCULAR         REFRACTION. 

As  previously  stated,  comparisons  form  a  most  valuable  method 
of  obtaining  knowledge,  and  this  applies  particularly  well  to  the 
practice  of  retinoscopy. 

Having  obtained  four  of  the  model  eyes  illustrated  by  figure 
134,  set  one  of  them  according  to  its  index  to   represent    etnmctropia. 

The  index  of  the  model  eye   will  be  found  to  read  as  follows  : — 
6";     4. ^21         o         123^56 


M'/OPIA. 


Hypermetropic 


The  figure  o  represents  emmetropia. 

Set  the  second  one  to  represent  myopia  of  one  dioptre;  the  third 
to  represent  myopia  of  four  dioptres:  and  the  fourth  to  represent 
hypermetropia  of  tivo  dioptres. 


Plate  140. 

Astigmatism  as  indicated  by  the  retinoscope,  the  typical  band   like  appearance  of  the  reflex 

in  the  pupil.     The  direction  of  the   light   band  indicates  the  location  of  the  two  principal 

meridians  of  the  refracting  system   of  the   eye,   therefore;  the   location  of  the  axis  of  the 

correcting  cylinder  lens. 

The  object  of  setting  the  eyes  to  represent  these  particular  con- 
ditions of  emmetropia,  and  ametropia  of  definite  character  and 
amount  is  this  :     Figures  129,  130,  131  and  132   illustrate  tlieoretically 


R  E  T  I   N  O  S  C  O  P  Y.  175 

these  definite  eonditio)is,  and  it  is  desired  to  show  hoiv  they  appear  to 
the  Refraetionist  under  aetual  working  conditions  ivith  the  retinoscope. 

A  small  shelf  should  be  fastened  to  the  wall  on  a  level  with  the 
operator's  eye,  upon  this  he  may  conveniently  place  the  model  eyes 
for  practice.  Place  the  four  model  eyes,  set  as  previously  directed, 
upon  this  shelf,  side  by  side  and  in  the  order  named.  Now  measure 
accurately  a  distance  of  one  metre  (forty  inches)  directly  in  front  of 
them.  This  will  represent  the  point  at  which  the  operator's  eye  must 
be  situated  for  the  examination.  A  very  convenient  procedure  will 
be  to  fasten  to  the  side  wall,  a  rule  marked  off  in  inches;  one  may  be 
obtained  at  a  small  cost;  or  a  mark  of  some  kind  may  be  placed  on 
the  wall  or  floor  to  indicate  the  position. 

The  operator  should  now  be  in  the  position  illustrated  by  plate 
135,  and  his  model  eyes  should  be  in  the  position  of  the  patient.  He 
is  now  ready  for  actual  work. 

Direct  the  light  beam  from  tr.e  retinoscope  full  upon  the  first 
eye,  set  to  represent  emmetropia.  By  the  term — full  upon  the  eye — 
the  condition  illustrated  by  plate  138  is  meant;  that  is,  the  pupil  is  in 
the  centre  of  the  light  area  on  t/ie  face;  in  plates  141,  142  and  143  the 
pupil  is  not  in  the  centre  of  the  light  area  because  the  light  beam  is 
not  full  upon  the  eye. 

When  the  light  beam  is  directed  full  upon  the  eye  and  held 
steadily  in  this  position,  the  black  appearance  of  the  pupil  will  in- 
stantly give  place  to  an  illuminated  appearance,  which,  as  previously 
stated,  is  called  the  luminous  pupil,  or  the  retinal  reflex,  usually 
shortened  to  simply  the  reflex.  This  appearance  of  the  reflex  in  the 
pupil  is  very  clearly  illustrated  in  plate  13S,  which  was  made  from  a 
photograph  from  life.  Compare  the  appearance  of  the  pupil  of  one 
eye,  illuminated  by  the  retinal  reflex,  with  the  pupil  of  the  other  eye 
which  appears  black. 

Now  direct  the  light  full  upon  the  second  eye,  and  hold  it  stead- 
ily. This  eye  represents  myopia  of  one  dioptre.  The  same  appear- 
ance of  the  pupil  will  appear  as  with  the  first  eye.  Submit  the  third 
and  fourth  eyes  to  the  same  conditions,  and  though  they  represent 
myopia  and  hypermetropia  respectively,  they  too  present  the  same 
appearance  as  the  other  eyes  under  like  conditions. 

Now  we  know  that  these  four  eyes  under  observation  represent 
four  different  conditions  of  refraction,  three  of  them  being  errors; 
yet  they  all  show  a  similar  appearance  when  the  beam  of  light  from 
the  retinoscope  is  directed  full  upon  them,  and  held  steadily  so.  The 
reflex  in  the  pupil  in  each  instance  shows  an  even  amount  of  illumin- 


176  OCULAR         REFRACTION. 

ation  and  fully  occupies  the  pupillary  area.  The  only  difference  that 
may  be  detected  will  be  a  difference  in  the  brilliancy  of  the  reflex, 
but  this  may  be  difficult  to  see,  and  would  not  serve  to  indicate  the 
character  of  the  refraction. 

When  the  light  area  is  full  upon  the  eye,  as  illustrated  by  plate 
138,  it  is  said  by  the  author  to  be  in  2.  primary  position,  when  it  is  in  a 
position  illustrated  by  plates  141,  142  or  143  it  is  said  to  have  moved 
to  a  Si-condary  position. 

Suppose  the  light  area  on  tiie  face  be  caused  to  move  completely 
across  the  pupil,  it  is  said  to  have  made  a  transit  of  the  pnpil. 

If  the  light  beam  from  the  retinoscope  be  swept  across  the 
model  eyes, arranged  side  by  side,  so  that  the  light  area  makes  a  tran- 
sit of  the  pupil  of  each,  it  will  be  observed  that  in  three  of  them  there 
is  a  movemen  of  the  retiex  in  the  pupillary  area.  In  one  of  them  there  will 
be  no  movement  op  the  refle.x. 

The  eye  in  which  there  appears  to  be  no  movement  of  the  reflex 
will  be  the  one  set  to  represent  myopia  of  ojie  dioptre.  This  absence 
of  movement  of  the  reflex  is  said  to  be  a  choked  appearance  of  the 
reflex.  //  occurs  t^'hen  the  eye  of  the  observer  with  the  retinoscope  is  at 
the  myopic  far  point  of  the  eye  under  examination;  the  area  of  illumin- 
ation on  the  retina  of  the  eye  under  examination,  and  its  image  at 
the  eye  of  the  observer  are  conjugate  to  each  other,  see  figure  127. 

During  the  transit  of  the  light  area,  in  the  pupils  of  the  three 
other  eyes  the  reflex  will  be  seen  to  move  also.  When  the  light  area 
reaches  its  primary  position,  see  plate  138,  the  reflex  will  be  seen  to 
illuminate  the  tvhole  pupillary  area.  When  it  reaches  a  secondary 
position,  see  plate  141,  it  will  be  observed  that  only  a  portion  of  the 
pupillary  area  is  illuminateJ,  the  remainder  being  in  darkness.  This 
area  of  darkness  in  the  pupil  which  appears  as  the  light  area  passes 
to  a  secondary  position  is  called  the  ''shadow; "  it  is  from  this  that  the 
term — "  Shadow  Test  "  is  derived. 

Plate  141,  represents  an  eye  under  observation,  in  which  the  light 
area  has  passed  from  the  primary  position  to  a  secondary  position, 
the  direction  in  which  the  light  area  moved  being  to  the  left.  The 
reflex  in  the  pupil  has  also  moved  to  the  lept,  the  right  half  of  the  pupil 
being  occupied  by  the  following  shadow.  The  direction  of  the  move- 
ment of  the  reflex  nas  therefore  been  the  same  as  that  of  the  light 
area;  in  other  words,  the  movement  of  the  reflex  is  ''with"  that  of 
the  light  area. 

Plate  142,  shows  the  light  area  in  a  secondary  position,  the  direc- 
tion of  its  movement  being  to  the  right,  the  movement  of  the  reflex 


R  E  T  I  N  O  S  C  O  P  Y.  177 

has  also  been  to  the  right,  or  "  ivitli  "  that  of  the  light  area. 

Plate  143,  shows  the  light  area  in  a  secondary  position,  the  move- 
ment being  to  tlic  right,  the  movement  of  the  reflex  in  this  instance  is 
to  the  left,  or  opposite  to  that  of  the  light  area.  It  is  said  to  be 
"  against"  that  of  the  light  area. 


Plate  141. 

Hypermetropia  as  indicaled  by  the  retinoKcope.     The  light  area  on   ihc  fnce  is  passing  off 

the  pupil   to  the   left,    the   movement   of  the   reflex  is  also  to  the  left  in  the  pupil,  with  the 

movement  of  the  light  area.       Theshado-v  is  seen  following  the  reflex  in  the  pupil. 

//  is  this  movement  of  the  rejie.x,  with  or  against  the  movetnent  of  the 
light  area,  that  ilctermines  the  character  oj  the  refraction  of  the  eye 

The  conditions  illustrated  by  figures  141,  142  and  143.  occur  when 
the  plane  mirror  retinoscope  is  operaietl. 

Now  sweep  the  light  beam  from  the  retinfiscope  acruss  the  four 
model  eyes  again,  and  observe  how  the  refle.x  moves  in  each.  In  the 
first  eye,  set  to  represent  emmetropia,  the  movement  will  be  "'  with"; 
in  the  second  eye  set  to  represent  myopia  of  one  dioptre  there  will  be 
no  movement,  the  reflex  being  "choked;"  in  the  third  eye,  set  to 
represent  myopia  of  four  dioptres  the  movement  will  be  "against  "; 
in  the  fourth  eye  set  to  represent  hypermetropia  of  two  dioptres  the 
movement  will  be  "  with".  From  this  the  following  rule  may  be 
established. 

With  a  plane  retinoscope,  at  a  working   distance    of   one    metre, 


I7S  OCULAR  R  E  F   R  A  C  T   I  O   N. 

myopia  of  over  one  dioptre  shows  movement  against  that  of  the  light 
area  Ilypermetropia,  einmetropia  or  myopia  of  less  than  one  di- 
optre shows  movement  with  that  of  the  light  area.  Myopia  of  one 
dioptre  shows  no  movement  of  the  reflex. 

Bear  in  mind  that  these  experiments  with  the  model  eyes  just 
outlined  are  the  practical  operations  involved  m  the  theory  illustrat 
ed  by  figures  129,  130,  131  and  132. 

In  first  operating  the  retinoscope  let  the  transit  of  the  light  be 
slow,  rapidity  is  acquired  with  practice.  If  the  untrained  eye  and 
mind  are  called  upon  to  see  and  interpret  the  movement  of  the  reflex, 
it  will  be  found  difficult  because  the  eye  will  see  more  quickly  than 
the  mind  can  interpret.  Mental  perception  is  slower  than  ocular 
perception. 

Havmg  observed  that  the  movement  of  the  refl:;x  in  the  first  eye 


Hyper 


ned  by 


p 

ate  I 

42. 

no 

cope, 
he  rig 

The  1 

ght   a 

rea   ami 

00 

D  S 

and 

the 

reflex 

reflex  bolh  passing  to 


with",  interpose  a  -f  i  00  U,  S.  and  the  reflex  will  be  found  to 
be  "choked"  because  the  emergent  parallel  rays  of  the  emmetropic 
eye  will  be  brought  to  a  focus  at  the  working  distance  of  one  metre. 
In  the  third  eye,  the  movement  of  the  reflex  "against"  will  be 
"  choked  "  by  interposing  a —  3.00  D.  S  ,  the  emergent  rays  which 
converged  to  a  focus    at    ten    inches    being    brought  to  a  focus  at  the 


R  E  T  I  N  O  S  C  O  P  Y. 


179 


working  distance  of  forty  inches.  The  fourth  eye  in  which  the 
movement  of  the  reflex  is  "  with  "  will  be  "choked  "  by  interposing 
a  +  3  00  D  S. ,  the  emergent  rays  which  diverged  being  brought  to 
a  focus  at  the  working  distance  of  one  metre. 


Myopia  as  indicated  by  tlie  relinoscope.       The  light  area  on  the  face  is  passing  cff  the  pupil 
to  the  right,  while  the  rtflex  ismoving  to  the  left  in  the  pupil. 

This  movement  of  tiie  retinal  reflex  in  the  pupillary  area,  with 
or  against  the  movement  of  the  light  area,  is  governed  by  the  follow- 
ing conditions  With  a  plane  retinoscope,  if  the  image  observed  is 
erect,  the  movement  will  be  "with";  if  the  linage  is  inverted  the 
movement  will  be  '•  against".  When  no  movement  occurs,  the  reflex 
being  "  choked",  the  reversal  point  of  the  image  is  indicated,  there- 
fore : — 

In  the  examination  of  an  eye  with  a  plane  retinoscope  if  the 
reflex  movement  is  against,  the  observer  is  beyond  the  reversal  point; 
if  the  movement  be  with,  the  observer  is  inside  of  the  reversal  point. 
It  will  be  seen  that  the  object  of  the  retinoscopic  examination  is  to 
locate  the  reversal  point  at  some  definite  working  distance. 

Roughly  estimated  it  is  usual  to  say  that  movement  against  indi- 
cates myopia,  movement  with  hypermetropia,  the  plane  mirror  being 
used.  If  a  concave  mirror  retinoscope  be  used  the  movement  of  the 
reflex  will  be  the    reverse    of   that  with  a  plane  retinoscope.     Move- 


iSo  OCULAR         R   E   F   K  A  C  T   I  O  N. 

ment  with  indicating  myopia,  movement  against  indicating  hyper- 
metropia. 

The  next  experiment  will  be  to  set  one  of  the  model  eyes  to 
represent  myopia  of  two  dioptres,  another  to  represent  myopia  of 
five  dioptres.  Pass  the  light  laeam  across  the  two  at  the  same  rate  of 
movement  and  observe  the  rate  of  movement  of  the  reflex  in  the  two, 
also  the  comparative  brilliancy  of  the  reflex.  It  will  be  found  that 
while  the  rate  of  movement  of  the  light  area  is  the  same,  that  the 
rate  of  movement  of  the  reflex  will  be  slower  in  the  eye  having  the 
greater  error.  The  reflex  will  be  brighter  in  the  eye  having  the 
lesser  error. 

Set  the  other  two  eyes  to  represent  hypermetropia  of  one  diop- 
tre and  four  dioptres  respectively  and  perform  the  same  experiment; 
a  similar  condition  will  be  noted  The  movement  of  the  reflex  will 
be  slower  in  the  case  of  the  greater  error,  and  the  reflex  will  be  less 
brilliant  in  the  eye  having  the  greater  error.  From  this  the  following 
observation  may  be  made. 

The  greater  the  error  of  refraction,  the  slower  the  movement  of 
the  reflex;  and  the  less  brilliant  will  it  be.  The  student  should  study 
these  differences  so  that  he  will  learn  when  a  high  or  a  low  power 
lens  is  indicated,  it  will  save  much  time  to  him  and  annoyance  to  his 
patient,  to  be  able  to  approximate  the  correcting  lens  by  the  rate  of 
movement  of  the  reflex.     This  too  is  acquired  with  practice. 

Suppose  we  consider  an  every-day  case.  The  retinoscope  indi- 
cates hypermetropia,  the  movement  being  "with".  As  the  student 
has  not  had  sufficient  practice  to  be  able  to  tell  by  the  rate  of  move- 
ment if  the  error  is  great  or  small,  it  will  be  suggested  that  he  place 
a  -}-  i.oo  D.  S.  before  the  eye  and  again  observe  the  reflex.  The 
movement  is  still  with.  What  has  he  now  learned?  That  it  is  a  true 
case  of  hypermetropia,  because  if  it  had  been  myopia  of  less  than  one 
diopcre  the  reflex  would  now  be  against;  while  if  it  were  emmetropia 
the  reflex  would  be  choked.  Replace  the  -[-  i.oo  D.  S.  with  a  +  2.00 
D.  S.  The  movement  is  still  with.  With  a  -f  3.00  D.  S.  the  move- 
ment appears  choked.  In  order  to  make  sure,  try  a.  -\-  3.50  D.  S.  If 
-f  3  00  D.  S.  did  choke  the  reflex,  with  the  +  3.50  D.  S.  there  will 
be  movement  against,  showing  that  the  reversal  point  has  been 
passed. 

In  order  that  one  may  be  sure  that  the  reflex  is  choked,  it  is 
always  well  to  go  beyond  the  reversal  point,  and  then  drop  back  to 
the  next  lens  weaker  than  the  one  which  reversed  the  movement  of 
the  reflex. 


R  E  T  I  N  O  S  C  O  P  Y.  iSj 

If  the  movement  be  choked  by  the  +  3  oo  D.  S.  it  is  known  that 
the  emergent  rays  are  now  converged  to  the  eye  of  the  observer  at 
the  working  distance,  in  this  instance  at  forty  inches.  Suppose  this 
was  the  right  eye  and  that  it  required  a -f  3.50  D.S.  to  choke  the  reflex 
in  the  left  eye.  Now  make  an  allowan;efor  the  working  distance  by 
adding  —  i.oo  D.  S.,  because  if  it  required  the  above  power  convex 
sphericals  to  converge  the  emergent  rays  to  forty  inches,  one  dioptre 
less  would  render  them  parallel,  or  create  conditions  similar  to 
emmetropia.     The  problem  would  then  be  as  follows:— 

O.  D.  +  3.00  D.  S.     Retinoscopic  findings. 

Add     —  1.00  D.  S.     Allowance  for  one  metre  working  distance. 
Correction  for  error  of  refraction. 


0. 

D. 

+  2.0c 

■D. 

S. 

0.  s. 

Add 

+  3-50 
—  1.00 

D. 

D. 

s. 
s. 

Retinoscopic  findings. 

Allowance  for  working  distance  of  one  metre 

O.  S.  +  2.50  D.  S.     Correction  for  error  of  refraction. 

Another  case  will  be  cited  for  illustration. 

The  person  is  of  advanced  age  and  the  pupils  are  quite  small. 
When  viewed  with  the  retinoscope  at  the  usual  working  distance,  one 
metre,  the  reflex  appears  dull,  and  its  movement  uncertain.  Ap- 
proaching nearer  to  the  patient,  say  twenty  six  inches,  the  direction 
of  the  reflex  seems  to  be  with,  indicating  hypermetropia.  +  3.00  D.S. 
interposed  renders  the  reflex  more  brilliant  and  increases  its  rate  of 
movement;  it  is  more  easily  observed  however  at  twenty-six  inches 
than  at  forty  inches,  so  twenty-six  inches  is  selected  as  the  working 
distance. 

It  is  found  that  a  -|-  6.50  D.  S.  appears  to  choke  the  reflex  in 
each  eye,  to  render  it  certain  -|-  7.00  D.  S.  is  interposed,  when  it  is 
found  that  the  direction  of  the  reflex  is  reversed,  showing  that  the 
reversal  p  lint  has  been  pissed.  The  estimate  of  the  error  and  its 
correction  will  be  as  follows:  — 

O.  U.  +  6  50  D    S.     Retinoscopic  findings. 

Add     —  [  50  D.  S.     Allowance  for  working  distance. 

O.  U.  +  5.00  D.  S      Correction  for  error  of  refraction. 

The  allowance  for  working  distance  is  one  and  a  half  dioptres 
because  it  is  the  equivalent  of  twenty  six  inches. 

It  may  be  observed  here  that  in  hypermetropia  the  pupils  are  apt 
to  be  smaller  than  if  the  error  be  myopia. 

In    examination  of  another   case  the   reflex   observed  from  a  one 


i82  OCULAR         REFRACTION. 

metre  distance  indicates  myopia,  the  movement  being  against  that  of 
the  lighi  area.  In  this  instance  the  following  is  the  estimate  of  the 
error: — 

O    D.  —  3  50  D.  S.     Retinoscop'c  findings. 

Ad  1    —  1.00  D.  S,      Allowance  for  working^distance. 

—  4.50  D.  S.     Correction  of  error  of  refraction, 

O.  S.  —  2.75  D.  S.     Retinoscopic  findings 

Add   —  1.00  D.  S.      Allowance  for  workmg  distance. 

—  3.75  D.  S.     Correction  of  err<  r  of^  lefraction. 

A  —  4.00  D.  S.  reversed  the  movement  of  the  reflex  in  the  right 
eye,  and  a  —  3.25  D.  S.  reversed  it  in  the  left  eye. 

In  making  the  allowance  for  the  working  distance  of  one  metre 
a  -—  1.00  D.  S.  is  added.  In  the  first  observation  of  the  eyes 
it  was  noted  that  the  emergent  rays  focussed  between  the  observer 
and  the  eye  under  observation.  The  concave  lenses  rendered  these 
convergent  rays  less  convergent  and  established  their  focus  at  forty 
inches.  By  the  addition  of  one  dioptre  more  concave  spherical  they 
would  be  rendered  parallel. 

By  some  writers  on  retinoscopy  the  operator  is  advised  to  sub- 
tract the  value  of  the  working  distance  in  hypermetropia,  and  add  the 
value  of  the  working  distance  in  myopia. 

It  will  be  found  less  confusing  to  remember  if  the  rule  is  made 
to  always  add  —  t  00  D.  S.  for  a  working  distance  of  one  metre.  If 
the  working  distance  be  twenty  inches,  of  course  add  —  2.00  D.  S., 
if  twenty  si.x  inches  add  —  i  50  D.  S.,  etc. 

Plate  144  illustrates  a  nice  point  in  retinoscopy,  the  estimation 
of  the  point  of  reversal  in  myopia  without  the  use  of  a  lens. 

The  preceding  cases  have  been  explained  to  show  that  the  point 
of  reversal,  or  myopic  far-point,  could  be  definitely  located  at  a  given 
working  distance.  If  an  eye  be  myopic  to  one  dioptre,  the  reflex  will 
appear  as  choked  at  forty  inches.  If  an  eye  be  myopic  to  more  than 
one  dioptre,  its  far-point  is  somewhere  inside  of  forty  inches;  if  the 
working  distance  be  moved  to  this  point.by  the  operator  approaching 
nearer  to  the  eye  than  the  one  metre  distance,  the  choked  appear- 
ance will  be  manifest  when  the  far-point  is  reached,  no  matter  how 
near  the  eye  it  may  be. 

For  example;  if  the  eye  be  myopic  to  four  dioptres,  its  far- point 
will  be  ten  inches  away.  At  forty  inches  the  reflex  will  move  against 
the  movement  of  the  light  area,  but  if  the  operator  approach   to  ten 


R   K  T   I  N   O  S  C  O  P  Y.  183 

inches  as  a  working  distance  the  reflex  will  appear  as  choked.     Near- 
er than  ten  inches  it  will  be  reversed. 

If  an  eye  be  myopic  to  eight  dioptres,  its  reflex  will  appear  as 
choked  at  five  inches;  if  myopic  to  three  dioptres,  choked  at  thirteen 
inches,  etc. 

From  this  it  will  be  observed  that  in  myopia  if  the  operator  will 
locate  the  far  point  of  the  eye  and  then  measure  his  working  distance, 
he  may  determine  the  refraction  without  any  lens  whatever. 

Plate  144  illustrates  a  method  for  working  in  this  manner.  The 
author  is  seen  operating  the  retinoscope  with  his  rij;ht  hand,  in  his 
left  is  held  a  spring  tape  measure  with  an  automatic  catch.  The 
patient  holds  the  end  of  the  tape-measure  against  his  cheek,  the  one 
inch  mark  being  in  line  with  his  eye.  The  end  of  the  tape-measure 
is  made  fast  to  a  convenient  handle  as  seen  in  the  illustration.  The 
working  distance  is  read  off  on  the  tape-measure,  when  the  reversal 
point  is  found,  and  quickly  transposed  into  dioptres.  This  illustra- 
tion is  given  in  order  to  show  the  accuracy  that  is  possible  with  the 
method,  and  therefore  its  value.  In  practice  it  will  not  be  necessary 
to  apply  this  in  all  cases,  but  if  the  operator  even  roughly  estimates 
the  myopic  far  point  by  approaching  the  eye,  and  then  workin.g  back 
to  his  one  metre  distance,  he  will  save  himself  much  time,  and  his 
patient  will  he  saved  annoyance  by  his  ability  to  select  approximately 
the  correcting  Itns  at  the  outset  of  his  examination. 

The  student  is  advised  to  practice  along  this  line  on  the  model 
eyes,  having  someone  make  the  eye  myopic  to  an  unknown  amount 
by  selecting  some  conv<x  lens  whose  value  is  unknown  to  him  and 
imposing  it  before  the  e\e 

In  order  to  be  sure  Ihrit  the  refle  x  is  perfectly  chi  ked  m  either 
hypermetropia  or  myopia,  a  transit  of  the  light  should  be  made  in 
various  meridians  <  f  the  eye  It  may  be  found  that  while  a  choked 
appearance  is  noted  in  some  meridians  that  in  others  there  will  still 
be  a  movement;  this  denote.-;  irregular  refraction 

Thus  far  only  spherical  errors  have  been  considered.  As  in  these 
cases  the  refraction  is  alike  in  every  meridian  it  make^  no  difference 
what  meridian  the  transit  of  the  light  follows.  When  the  refraction 
of  one  meridian  is  ascertained,  all  are  known. 

In  astigmatic  conditions  the  procedure  is  obviously  quite  differ- 
ent. In  neutraliz'ng  an  unknown  astigmatic  lens,  it  is  necessary  to 
locate  its  two  principal  meridians  and  then  ascertain  the  dioptric 
value  of  each. 

In   astigmatism  it  is   necessary  to  locate  the  two  principal  meri- 


i84  OCULAR         REFRACTION. 

dians  of  the  eye,  then  measure  the  refraction  of  each. 

The  astijimatic  band  seen  in  the  reflex,  illustrated  in  plate  140, 
indicates  the  position  o'  the  two  principal  meridians.  One  of  them 
will  be  parallel  to  the  direction  of  the  band,  the  other  will  be  at  right 
angles  to  it.     In  plate   140,   the  principal   meridians  are   indicated  i^ 


11  so  Mm  s^ni^^H^I 

II  ^  ^  ^    llllll  ^  ^  11  iH^^^^Hi 

SI            alllH  v^-  a  lUHIPIII^^^Hl 

11^      W^  ^^      tsH^jj/t^^^m 

WL 

i 

I^^^F^^    ^  <-^^^^^K[^              ^dHI^IBi 

Plate  144. 

Method  of  locating  the  myopic  far  point  in  myopia   without  the  aid  of 
the  working  distance  with  a  tape  measure  held  by  patient  and  operator 
in  the  author's  refracting  room. 


R  E  T  I  N  O  S  C  t)  P  Y. 


185 


the  vertical  and  horizontal  directions.  In  measuring  the  refraction 
of  an  astigmatic  eye,  the  transit  of  the  light  must  follow  these  two 
meridians  and  no  others. 

Plate  145,  illustrates  astigmatism  at  an  oblique  axis,  the  light 
band  is  seen  passing  from  the  pupil  and  followed  by  the  shadow,  the 
straight  band  of  separation  is  clearly  shown. 

Suppose  that  in  the  retinoscopic  examination  of  an  eye  the  ap- 
pearance of  the  reflc.x  in  the  pupil  is  similar  to  that  shown  in  plate 


Plate  145- 
Astigmatism  at  an  oblique  angle.     The  light  band  is  seen  just  leaving  the  pupil. 

140.  If  a  transit  of  the  light  in  the  direction  of  the  band,  shows 
slight  movement  witli  the  movement  of  the  light  area,  hypertnetropia 
is  indicated  in  that  meridian.  If  a  transit  of  the  meridian  at  right 
angles  to  the  band  shows  movement  of  the  light  band  against  X.\i^ 
movement  of  the  light  area,  myopia  is  indicated  in  that  meridian. 
The  working  distance  being  one  metre. 

Interpose  a  +  1.00  D.  S  ,  and  it  will  be  assumed  that  this  chokes 
the  refle.x  in  the  horizontal  meridian.  Now  the  vertical  meridian 
showed   myopia    before    any    lens    was    interposed,  the  -^  1.00  D.  S. 


i86  OCULAR         REFRACTION. 

therefore  renders  this  meridian  more  myopic.  No  matter,  leave  the 
+  1.00  D.  S.  before  the  eye. 

Concave  value  is  wanted  in  the  vertical  meridian,  but  it  is  desired 
not  to  disturb  the  horizontal  meridian  in  which  the  reflex  is  choked 
by  the  +  i.oo  U  S.  This  may  be  accomplished  by  using  a  concave 
cylinder  and  placing  the  axis  parallel  to  the  meridian  in  which  the 
reflex  is  choked :  that  is,  parallel  to  the  direction  of  the  light  band,  or 
its  axis  horizontal.  It  will  be  assumed  that  a  —  2.50  D.  Cyl.  chokes 
the  refle.x  in  the  vertical  meridian,  in  fact,  with  the  +  1.00  D.S.  3  — 
2.50  D.  Cyl.  ax.  <8o°,  the  reflex  is  choked  in  all  meridians  of  the  pupil. 

What  is  understood  to  be  tne  condition  now  ?  Simply  this,  the 
rays  of  light  that  emerged  from  the  eye  irregularly,  are  now  con- 
verged regularly,  and  brought  to  a  focus  at  the  working  distance  of 
forty  inches. 

In  making  the  allowance  for  the  working  distance  the  same  pro- 
cedure is  followed  as  in  spherical  errors  of  refraction,  add  —  i  00  D.  S. 
to  the  retinoscopic  findings.     In  this  instance:- — 

-j-  T.oo  D.  S.  3  —  ^-5°  D.  Cyl.  ax.  180°     Retinoscopic  findings. 
—  1.00  D    S  Allowance  for  working  distance  of  one  metre. 

03  —  2.50  U.  Cyl.  ax.  180°  Correction  for  error  of  refraction. 

It  will  be  seen  that  in  this  particular  case  the  correction  is  re- 
duced to  a  plane  concave  cylinder.  The  allowance  for  working  dis- 
tance does  not  alter  the  cylinder,  it  only  affects  the  spherical. 

This  point  is  frequently  confusing  to  the  student,  he  does  not  see 
why  it  should  not  also  affect  the  cylinder.  If  he  will  stop  to  think 
that  the  combination  of  spherical  and  cylinder  was  required  to  bring 
the  irregularly  emergent  rays  to  a  regular  convergence  and  focus,  he 
will  see  that  this  regularity  of  direction  must  not  be  disturbed  in 
estimating  the  combination  of  spherical  and  cylinder  required  to 
make  the  emergent  rays  parallel. 

The  following  examples  may  serve  to  make  this  clear.  Working 
distance  (W.  D. )  i  metre. 

Ret.  Find. 

W.  D.  1  metre. 

Correction. 

Ret.  Find. 
W.  D.  I  metre. 
+  2.50  D.  S   3 —  '-25  ^-  ^y'-  ''•''    '5^     Correction. 


4-  2.00  D.  S.  3  —  3-00  D.  Cyl.  ax. 
—  I  00  D.  S 

'65 

4-^1.00  D.  S.  3  ^  3-0°  D.  Cyl.  ax. 

+  3-5°  D.  S.  C  —  1.25  D.  Cyl.  ax. 
—  1,00  D.  S. 

165 

■5" 

R  E  T  I  N  O  S  C  O  P  Y,  187 

Ret.  Find. 

W.  D    I  metre. 

Correction. 

Ret.  Fii.d. 

W.  D.  26  inches. 

Correction. 

Ret    Find. 

W.  D.  40  inches. 

Correction. 

Ret.  Find. 

W.  D.   I  metre. 


—  1.50  D.  S.  C  — 0-75  D.  Cyl. 

—  1.00  D.  S. 

ax.  90° 

—  2.50  D.  b.  C  —  0.75  D.  Cyl. 

—  3.50  D.  S.  C— 2.25  D.  Cyl. 

—  1.50  D.  S. 

ax.  90° 
ax.  10° 

—  5  00  D.  S.  C  —  2  25  D.  Cyl 

-  .50  D.  Cyl 

—  1.00  D.  S. 

.  ax.  ,0° 
.  ax.  iSo° 

—  1.00  D  S.  C—  1  50  U  <->!• 
+  2,00  D.  S.  C  —  I  CO  D.  Cyl 

—  I.OO  D.  S. 

ax.  iSo° 
.  ax.  80' 

+  I  00  U.  S.  C^ —  1.00  U.  Cyl.  ax.  80°     Correction. 

In  cases  of  simple,  and  compound  myopic  astigmatism,  little 
difficulty  is  experienced  in  making  the  retinoscopic  estimate  of  the 
error 

If  it  be  simple  myopic  astigmatism,  a  plane  concave  cylinder  may 
be  used  to  create  the  choked  appearance  of  the  reflex,  the  axis  being 
placed  parallel  to  the  direction  of  the  light  band.  Or,  knowing  that 
in  the  meridian  parallel  to  the  light  band  the  eye  measures  emme- 
tropic, the  refraction  of  the  meridian  of  error,  at  right  angles  to  it, 
may  be  measured  by  imposing  a  concave  spherical. 

If  the  case  be  one  of  coinpound  myopic  astigmatism,  the  meridian 
of  least  error  will  be  corrected  by  a  concave  spherical,  the  other  prin- 
cipal meridian  will  require  a  concave  cylinder  in  addition  to  the  spher- 
ical already  imposed. 

The  cases  that  tax  the  skill  of  the  refractionist  are  those  that  be- 
long to  the  following  classes;  simple,  and  compound  hypermetropic 
astigmatism,  and  mixed  astigmatism.  The  reason  for  this  is,  that  the 
action  of  the  accommodation  must  be  controlled.  In  myopic  astigma- 
tism this  annoying  factor  is  in  the  majority  of  instances  absent. 

The  secret  of  success  lies  in  the  use  of  a  method  similar  to  that 
employed  in  the  subjective  method  known  as  the  "  fogging  system," 
viz: — the  use  of  convex  lenses. 

The  method  will  be  most  readily  understood  if  the  procedure  in  a 
case  of  mixed  astigmatism  be  explained. 

Refer  to  figure  140  again  and  assume  that  in  a  transit  of  the  hori- 
zontal meridian  the  movement  is  with,  indicating  hypermetropia.  A 
transit  in  the  vertical  meridian  shows  the  reflex  movement  against, 
showing  myopia.       In  such  a  case   three  different  methods  of  locating 


i8S  OCULAR         REFRACTION. 

the  myopic  far  point  with  combinations  of  lenses  may  be  followed,  all 
of  which  will  be  correct.     They  are  as  follows: 
4-  Spherical  3  —  Cylinder. 

—  Spherical  3  +  Cylinder. 

—  Cylinder  Q  -f-  Cylinder. 

While  any  one  of  these  three  combinations  if  properly  estimated, 
will  be  correct,  and  the  optical  effect  of  all  be  the  same,  provided  they 
are  properly  worked  out,  still  there  is  a  preference  as  to  which  one  to 
follow.  It  is  the  first  one  given,  a  convex  spherical  combined  with  a 
concave  cylinder. 

By  first  imposing  the  convex  spherical  that  chokes  the  hyperme- 
tropic movement,  the  desire  to  accommodate  ceases  and  the  accommo- 
dation is  relaxed.  The  convex  spherical  should  remain  before  the  eye 
and  the  required  concave  cylinder  be  added  to  correct  the  other 
meridian. 

From  this  procedure  the  following  rule  may  be  established. 
In  mixed  astigmatism,  correct  the  hypermetropic  meridian  with  a 
convex  spherical  first,  then  correct  the  myopic  meridian  with  a  concave 
cylinder. 

Example. 

4-  2.75  D   S  3  —  4  oo  D.  Cyl.  ax.  40°     Ret.  Find. 

Add  —  I  00  D.  S. Allowance  for  W.  D.  4o  inches. 

-\-  1.75  D.  S.  3  —  4°°  D.  Cyl.  ax.  40°     Correction. 
In  compound  hypermetropic  astigmatism,  the  same  practice  should 
be  followed  according  to  the  following  rule. 

Correct  the  meridian  of  most  hypermetropia  with  a  convex  spher- 
ical first,  then  correct  the  other  meridian,  which  has  been  made  myopic 
with  a  concave  cylinder. 
Example. 

+  4.0c  D.  S.  C  —  '-oo  D.  Cyl.  ax.  iSo°     Ret.   Find. 
Add  —  1.00  D.  S.  Allowance  tor  W.  D    40  inches. 

-{-  3.00  D.  S.  O  —  ^■°°  D.  Cy].  ax.  180°     Correction. 
This  should  be  transposed  to  its  equivalent  generic  value. 
4-  2.00  D.  S.  3  +  ^■°°  D.  Cyl   ax.  90° 
It  may  be   said  that  the   same  result  could  be  obtained  by  correct- 
ing the  meridian  of  least  hypermetropia  first  with  a  convex  spherical, 
and  then  the  other  meridian  with  a  convex  cylinder,  arriving  at  a  gen- 
eric formula  at  first.     So  it  could  be  done,  but  by  making  the  estimate 
with  a  contra-generic  formula,  which  is  easily  transposed  into  its  gen- 


R  E  T  I  N  O  S  C  O  P  Y.  189 

eric  equivalent,  the  results  may  be  more  quickly  and  accurately 
obtained;  the  accommodation  being  relaxed,  or  rather,  held    in    check. 

It  will  be  a  valuable  rule  to  follow,  to  always  impose  a  convex 
spherical  lens  whenever  any  hypermetropia  is  manifest,  even  though  it 
may  be  of  small  amount  compared  to  the  manifest  myopia. 

Contra-generic  formula  of  convex  spherical  combined  with  concave 
cylinder,  makes  reliable  results  possible  with  the  retinoscope  without 
the  aid  of  a  cycloplegic. 

There  will  be  noticed  in  some  cases  a  peculiar  appearance  of  the 
reflex;  when  the  light  beam  is  full  upon  the  eye,  the  light  area  being  in 
the  primary  position,  the  reflex  may  appear  as  illustrated  by  plate  140, 
the  characteristic  astigmatic  light  band.  When  the  light  area  is  moved 
to  a  secondary  position,  the  light  band  may  appear  to  be  divided  into 
two  bands,  that  approach  or  separate  as  the  light  transit  is  made  in  a 
meridian  at  right  angles  to  their  diiection.  The  effect  created  is  called 
the  "  scissors  motion  "  of  the  reflex.  It  is  due  to  irregular  astigmatism 
and  usually  indicates  a  contra-generic  correction  of  convex  spherical 
combined  with  a  stronger  concave  cylinder. 


CHAPTER  VII. 

PRACTICAL  HINTS  FOR  THE  PRACTICE  OF  RETINOSCOPY. 

Tt  is  advisable  to  interpose  lenses   before  bath  eyes  at  the  same  time 
■^       in  locating  the  reversal  point  at  the  working  distance.       By  this  it 

is  meant  that  it  is  not  desirable  to  use  a  blank  disk  over  the  asso- 
ciated eye  while  making  the  retinoscopic  examination  of  the  other. 
Impose  the  necessary  lenses  before  each  eye,  working  toward  the  re- 
quired corrections  simultaneously. 

If  the  case  under  examination  be  hypermetropia,  simple  or  com- 
pound, one  eye  may  have  a  convex  spherical  imposed  that  is  stronger 
than  is  required  for  the  correction  of  the  error,  while  the  proper  cor- 
rection for  its  associated  eye  is  being  made.  This  tends  to  relax  the 
accommodation  and  incidently  to  expand  the  pupils  of  both  eyes 

In  myopia  a  partial  correction  of  the  error  of  one  eye  while  the 
fuUe  correction  for  the  associated  eye  is  being  made  with  the  retinos- 
cop  ,  relieves  the  ocular  strain  that  may  occur  if  one  eye  is  occluded 
during  the  examination  of  the  other,  or  only  one  eye  is  corrected  at  a 
time.  A  very  desirable  condition  if  the  person  is  of  a  nervous  temper- 
ament. 


If  the  light  beam  from  the  retinoscope  is  so  directed  upon  the  eye 
that  the  area  of  illumination  on  the  retina  covers  the  yellow  spot  (mac- 
ula), it  may  prove  annoying  to  the  patient  and  further  contract  the 
pupils,  therefore,  direct  the  patient  not  to  look  at  the  retinoscopic  mir- 
ror but  to  either  side  of  the  operator's  liead  or  just  over  his  head.  A 
desirable  position  for  the  patient  to  assume  is  to  have  him  face  the 
operator  squarely,  with  the  head  inclined  slightly  downward,  and  his 
vision  fixed  upon  some  object  just  over  and  behind  the  head  of  ihe 
operator. 

This  position  throws  the  area  of  illumination  upon  a  portion  of  the 
retina  sufficiently  near  to  the  centre  of  perception  (the  macula)  to 
obtain  the  best  results  without  causing  the  patient  any  discomfort. 


The  retinoscopic  examination  should  be  conducted  as  speedily  as 
is  consistent  with  accurate  work,  if  it  is  too  prolonged  it  will  prove  as 
annoying  as  a  lengthy  subjective  test. 


PRACTICAL    HINTS   F  O  R  ;  T  H  F.  P  R  A  C  T  1  C  K  O  F  R  E  T  I  N  O  S  C  O  P  Y. 

Nervous  patients  often  ask  il  the  strong  light  from  the  retinoscope 
will  harm  the  eye,  They  may  be  reassured  by  telling  them  that  it  is 
harmless,  the  effect  of  the  glare  passing  quickly  away  after  the  exam- 
ination. 


A  retinoscope  in  which  the  peep-hole  is  drilled  through  the  glass 
frequently  shows  annoying  reflections  from  the  edge  of  the  hole;  it 
causes  a  peculiar  spider  web  effect  of  light  that  interferes  with  the  view 
of  the  reflex.  In  selecting  an  instrument  care  should  be  exercised  to 
see  that  this  defect  does  not  exist.  Some  instruments  do  not  have  the 
hole  in  the  glass,  the  peep-hole  being  made  through  the  silver  backing 
of  the  mirror  only,  this  obviates  the  above  defect  but  does  not  permit 
as  much  of  the  emergent  light  to  reach  the  eye  of  the  observer  as 
where  the  glass  is  drilled. 


As  the  reversal  point  is  reached,  particularly  in  cases  of  high 
myopia  and  high  hypermetropia,  or  when  the  pup'ils  are  large,  it  may 
be  observed  that  in  the  central  portion  of  the  pupil  the  reflex  will  ap- 
pear to  be  choked,  while  in  the  peripheral  portions  of  the  pupil  there 
may  still  appear  to  be  movement.  If  a  lens  be  imposed  that  will  choke 
the  peripheral  portions,  movement  may  still  occur  in  the  central  por- 
tion of  the  pupil. 

This  is  due  to  the  spherical  abberation  of  tlie  eye,  and  interferes 
with  the  retinoscopic  estimate  of  the  error  to  more  or  less  degree.  As 
the  central  portion  of  the  pupil  is  most  nearly  concerned  in  vision,  base 
the  estimate  upon  the  lens  required  to  choke  the  reflex  in  the  centre  of 
the  pupil. 


If  the  reflex  shows  an  irregular  movement  in  the  pupil,  the  light 
area  in  the  pupil  being  broken  up  into  little  patches  of  varying  brilli- 
ancy which  move  in  different  directions  as  a  transit  of  the  light  beam 
is  made,  a  condition  of  irregular  refraction  in  the  refracting  system  of 
the  eye  is  indicated.  This  seriously  impairs  'he  value  of  the  retino- 
scopic examination.  In  such  cases  it  will  be  usual  to  find  that  the 
visual  acuity  is  sub-normal  and  incapable  of  being  raised  to  normal 
with  any  lens.     Conical  cornea,  corneal  scars,  etc.  cause  this  condition. 


In  younger  persons  the  pupils  are  apt  to  be  large,  this  exposes  a 
large  area  of  the  refracting  system  of  the  eye.  As  nearly  all  eyes 
possess  a  little  astigmatic  error,  as  the  reversal  point  is  reached  in  the 
retinoscopic  examination,  this  astigmatism  becomes  manifest,  it  may 
be  regular  or  irregular  and  may  prove  confusing   to   the  operator.     It 


Ig2  OCULAR         REFRACTION. 

may  happen  that  a  weak  cylinder  seems  indicated  at  a  certain  axis,  yet 
on  proving  the  estimate  subjectively,  'he  operator  may  find  that  the 
patient  demands  that  the  axis  be  at  the  opposite  position  that  was^ 
estimated  with  the  retinoscope.  Some  have  condemned  the  retinos- 
cope  for  this  apparent  failure  but  it  is  the  operator  who  is  to  blame, 
not  the  instrument.  This  can  only  occur  with  weak  cylinders  and  will 
not  occur  when  the  operator  acquires  skill  and  experience. 


The  introduction  of  the  luminou  .  retinoscope  into  the  practice  of 
retinoscopy  has  widened  the  field  of  the  retinoscopic  test;  it  makes  it 
possible  to  obtain  a  reflex  of  sufficient  brilliancy  under  all  conditions 
for  the  observer  to  see  it.  If  a  reflex  may  be  obtained  that  it  is  possi- 
ble for  the  refractionist  to  see,  he  will  be  enabled  to  apply  the  test. 

This  form  of  instrument  is  a  great  help  to  the  student,  the  author 
finding  it  most  valuable  in  his  work  as  an  instructor  of  ocular  refrac- 
tion. 


In  this  book  the  student  will  doubtless  note  the  absence  of  any 
instructions  regarding  Subjective  work  with  the  Test  Case.  This  must 
not  be  construed  to  mean  that  the  author  undervalues  this  work,  nor 
overestimates  the  value  of  Objective  methods.  In  correcting  ocular 
errors  of  refraction  the  two  methods  should  be  employed  in  every  case, 
(excepting  those  cases  of  young  children,  illiterates,  etc.)  each  serving 
to  verify  the  findings  of  the  other  and  thus  tending  toward  greater 
accuracy. 

The  demand  for  accurately  adapted  lenses  for  the  eye  is  growing, 
and  greater  exactitude  is  required  of  the  refractionist.  In  justice  to 
his  patient,  as  well  as  for  his  own  material  benefit,  all  methods  of  value 
should  be  practiced.  As  stated  in  the  beginning  of  this  work,  the 
author  believes  that  Retinoscopy  is  the  most  valuable  of  all  methods 
and  should  be  given  preference,  but  its  findings  should  be  checked  up 
by  subjective  work  with  the  test  case.  This  statement  must  not  be 
taken  as  an  admission  of  inaccuracy  of  the  retinoscopic  findings;  their 
value  depends  upon  the  skill  of  the  operator. 

So  much  has  been  written  of  Subjective  work  that  it  is  not  deemed 
necessary  to  include  it  in  this  book. 


GLOSSARY    OF    TECHNICAL    TERMS 


Tlie  following  list  includes  all  the  technical  terms  used  in  this  work,  as  well 
as  others  in  frequent  use  in  optical  literature : 


Abduction,  power  of.  The  term  used  to  describe  the  effort  required  to  unite  two 
images  created  by  placing  a  prism  base  inw-ard  before  the  eyes.  The  strongest 
prism  so  overcome  is  the  measure  of  the  strength  of  the  external  recti.  The 
normal  measure  of  strength  is  7°  to  8°. 

Abf.rr.vtion  (.-/  wandering  away).  _  In  optics  used  to  describe  the  deviation  of  light 
ray-.    Sci-  Spherical  Aberration  and  Chromatic  Aberration. 

ArniMMiiiiAiKix.  The  function  by  which  the  eye  is  capable  of  increasing  its  refrac- 
ti'.iu,  thus  focusing  for  far  and  near. 

AcHKu.MATiL  iHithoiit  color).  The  term  used  to  describe  a  lens  corrected  for 
chromatic  aberration. 

Achromatopsia.     Total  color-blindness. 

Acuity  of  Vision-.     ^Measure  of  sensibility  of  sight. 

Adduction,  power  of.  The  effort  required  to  fuse  two  images  created  by  placing  a 
prism  base  outward  before  the  eyes.  The  strongest  prism  so  overcome  is  the 
measure  of  strength  of  the  internal  recti.  The  average  normal  strength  is  18° 
to  24°. 

Amblyopia.  Sub-normal  visual  acuity;  it  may  be  congenital,  or  an  acquired  con- 
dition. 

Ametropia.  Abnormal  conditions  of  refraction;  all  errors  of  refraction  are  classed 
under  this  one  head. 

Amplitii'K  ni  A' I  nM  mchation.  The  measure  of  the  power  of  accommodation, 
usuall\   I  \|.n-^i(l  in  dioptres.     It  varies  according  to  age. 

AnisometudI'ia,     a  marked  difference  in  the  refraction  of  two  associated  eyes. 

Aperture  of  a  lens  or  mirror.  The  diameter  of  a  lens  or  mirror  available  for 
optical  purposes  of  refraction  or  reflection. 

Aphakia.  The  condition  of  the  eye  when  the  crystalline  lens  has  been  removed,  as 
after  operation  for  cataract. 

Aqueous.     The  watery  humor  of  the  eye. 

Arcus  Senilis  (A  bozv  of  the  aged).  A  white  ring  that  appears  around  the  outer 
edge  of  the  cornea  in  elderly  people. 

Asthenopia  (]]'cakne.<:.^).  ,\  muscular  weakness.  It  is  of  two  classes:  Accommo- 
dative Asthcnopi,!,  \\(:ikiu';s  of  the  ciliary  muscles;  Muscular  Asthenopia, 
weakness  of  tlu  \w\:.y  iim^cles.  It  is  manifest  in  ocular  distress  in  reading 
and  close  point  .iiiplicatioii. 

Astigmatism.  l)escn|.ii\  l-  ..l  cnndition  of  unequal  refraction  in  various  meridians  of 
the  eye.  ami  reijuiring  a  cylinder  lens  for  its  correction. 

Atrophy  (]\\islin;j,) .  \  condition  brought  about  by  lack  of  proper  nourishment  to 
the  eye.  caused  li}   poison,  etc.     See  Toxic  Amblyopia. 

Axis.     An  imagmary  lino  about  which  a  body  turns. 

Balance  of  the  E.xtra-Ocular  Muscles.  Proper  comparative  strength  of  the 
motor  muscles. 

Binocular  \'isiox.     Single  perception  with  two  eyes. 


194  OCULAR         REFRACTION. 

Blind  Spot.     The  point  of  no  vision  on  the  retina.     Where  the  optic  nerve  pierces 

the  retina. 
Canthus.     The  angle  where  the  eyehds  meet ;  in  each  eye  there  i>  the  inner  and  onter 

canthus. 
Cat.^ract.     An  opacity  of  the  crystalHne  lens,  usnally  acquired   in  old  age;  some- 
times congenital. 
Choked  Reflex.     The  appearance  of  the  retinal  reflex  in  retinoscopy  wlien  the  point 

of  reversal  is  reached,  no  movement  being  seen. 
Choroid.     The  middle  coat  of  the  eye. 
Choroiditis.     Inflammation  of  the  choroid. 
Chromatic  Aberration.     Dispersion  of  light  due  to  unequal  deviation  of  the  rays 

by  refraction. 
Coloboma.     a  rent  or  fissure  of  the  membranes  of  the  eye. 
Concomitant  Sijiixt.     Tliat  condition  in  which  one  eye  deviates  from  the  point  of 

fixation.   \  ct   retains   its  visual   power;   if  the   dominant  eye   be  coxered,   the 

deviating  lye  will  I'lx  the  object  seen. 
Co.vgenital.     Existing  at  birth. 
Conjunctiva.     JNIucous  membrane  lining  the  eyelids  and  e-xtending  contimmusly  over 

the  exposed  portion  of  the  eyeball. 
Conjunctivitis.     Inflammation  of  the  conjunctiva. 
Conjugate  Foci.     Two  points  so  related  that  rays  of  light  emanating  from  one  and 

refracted  by  a  convex  spherical  lens  focus  at  the  other.     Their  positions  are 

interchangeable. 
Convergence.     The  power  by  which  the  eyes  are  turned  inward  to  observe  an  object 

at  a  near  point. 
Cornea.     The  outer,  transparent  portion  of  the  eye. 
Cover  Test.     See  Test. 

Crystalline  Lens.     The  double  convex  lens  of  the  eye  forming  part  of  the  refract- 
ing system  of  the  eye,  and  capable  of  increasing  its  power  of  refraction.     Part 

of  the  apparatus  of  accommodation. 
Cvclitis.     Inflammation  of  the  ciliaries. 
Cycloplegia.     Paralysis  of  the  ciliary  muscles. 
Dioptre.     The  unit   of  measure   for  lenses  based  upon  the  metric  system.     .\  lens 

having  a  focus  of  approximately  40  inches. 
Diplopia.     Double  vision. 
Disk,  The.     Sometimes  used  to  designate  the  head  of  the  optic  nerve  as  seen  with 

the  ophthalmoscope. 
Emmetropia.     That  condition  of  tlie  eye  in  which  normal  conditions  of  refraction 

exist. 
Enucleation.     A  removal  of  the  eye. 
Epiphora.     Excessive   flow   of   tears,    watering    of   the   eye.     Usually   caused   by   a 

partial  or  complete  stoppage  of  the  tear  duct. 
Errors  of  Refraction.     Abnormal  conditions  of  refraction  in  tb.e  eye. 
EsoPHORiA.     A  tendency  of  the  visual  line  inward. 
Esotropia.     A  turning  inward  of  the  eye. 
ExoPHORiA.     A  tendency  of  the  eye  to  turn  outward. 
ExoTROPiA.     A  turning  of  the  eye  outward. 
Extra-Ocular  Muscles.     The  motor  muscles. 
Far  Point.     The  point  from  which  the  eye  in  a  state  of  rest  is  adapted  t<i  receive  and 

focus  rays  of  light  upon  its  retina.     Punctum  Remotum. 
Field  of  Vision.     That  portion  of  space  perceptible  to  the  eye  at  one  time :  that  is, 


GLOSSARY  195 

without  its  shifting  the  point  of  fixation. 
Focus   (A  Hre  place).     The  point  at  which  rays  of  light  meet  after  refraction  by  a 
lens,  or  reflection  by  a  mirror. 

Foramen,  Optic.  Opening  into  the  orbital  cavity  through  which  the  optic  nerve  and 
central  artery  reach  the  eye. 

FovE,\  Centralis.  A  small  depression  in  the  macula,  where  the  retina  is  most  sensi- 
tive to  vision.  Where  the  line  of  vision  meets  the  retina  under  normal 
conditions  without  an  effort. 

Fundus.  The  eye  ground.  Seen  with  the  ophthalmoscope.  It  includes  the  optic 
nerve,  arteries,  etc. 

Generic  Compounds.  Lenses  having  spherical  and  cylindrical  curvature  of  the  samo 
species ;  that  is,  both  convex,  or  both  concave.  Contra-generic  compounds 
have  one  surface  convex,  the  other  concave. 

Gl.\ucom.\.  a  disease  of  the  eye  in  which  there  is  an  abnormal  increase  in  the  con- 
tents of  the  globe,  causing  excessive  tension.  The  pupil  is  sluggish  and 
assumes  a  sea  green  tint ;  hence  the  name. 

Granulated  Eyelids.     Granular  conjunctivitis. 

Hemeralopia.     Day  vision,  or  night  blindness. 

Heterophoria.  An  imbalance  of  the  motor  muscles  of  the  eye.  A  tendency  of  the 
visual  line  of  one  eye  to  deviation  from  the  other. 

Heterotropia.     An  actual  deviation  of  the  visual  lines  from  parallelism. 

Homonymous  Diplopia.  Double  vision  in  which  the  two  images  occupy  the  same 
relative  positions  regardless  of  the  direction  of  the  look. 

Hypermetropia  {The  far-sighted  eye).  The  hypermetropic  eye  possesses  equal 
refraction  in  every  meridian,  but  the  retina  is  situated  between  the  refracting 
system  and  its  principal  focus. 

Hyperphoria.     A  tendency  of  deviation  of  the  visual  line  of  one  eye  above  the  other. 

Hypertropia.     a  deviation  of  the  visual  line  of  one  eye  above  the  other. 

Illuminated  Bodies.     Those  that  receive  light  from  other  bodies. 

Image,  Optical.     An  appearance  of  an  object  created  by  refraction  or  reflection. 

Index  of  Refraction.  The  relative  resistance  offered  to  the  passage  of  light  rays 
by  various  transparent  media  as  compared  to  that  of  air. 

Inferior  Recti.     The  motor  muscles  that  give  the  eye  a  downward  direction. 

Internal  Recti.     The  motor  muscles  that  operate  to  turn  the  eyes  inward. 

Iridectomy.  The  cutting  away  of  a  portion  of  the  iris.  Performed  in  glaucoma, 
cataract  operations,  etc. 

Iris.  A  circular  membrane  that  acts  as  a  diaphragm  to  regulate  the  amount  of  light 
that  enters  the  eye  through  the  pupil.     That  which  gives  tc  the  eye  its  "color." 

Ibis  Shadow.  The  test  for  maturity,  or  ripened  cataract ;  created  by  oblique  illumi- 
nation. 

Iritis.     Inflammation  of  the  iris. 

Jaeger's  Test  Type.     The  standard  type  for  close-point. 

Keratitis.     Inflammation  of  the  cornea. 

Lens.     An  optical  instrument  for  the  regular  refraction  of  light  according  to  system. 

Light.     A  form  of  energy. 

Light  Area  on  the  Face.  The  term  used  to  designate  the  light  upon  the  face  when 
the  beam  of  light  from  the  retinoscope  is  directed  upon  the  eye  under  obser- 
vation. ,        ,  • 

Light  Area  in  the  Pupil.  The  light  seen  in  the  pupil  of  an  eye  under  obseivation 
with  the  retinoscope,  caused  by  the  reflex  from  the  retina.  Its  character  and 
relative  movement  indicate  the  refraction  of  the  eye. 


Ig6  OCULAR        REFRACTION. 

Luminous  Bodies.     Those  sources  of  direct  light,  as  the  sun,  a  hghted  candle,  etc. 

Luminous  Pupil.  The  appearance  of  the  pupil  under  observation  with  the  retino- 
scope. 

Macul.\  Lutea.     The  "yellow  spot"  or  region  of  greatest  sensitiveness  of  the  retina. 

Maddox  Rod.     An  optical  devi:e  to  determine  the  tendency  of  the  visual  lines. 

Media.     The  refracting  humors  of  the  eye. 

Meridian.     A  great  circle  that  divides  the  sphere  into  two  equal  hemispheres. 

Miosis.     An  abnormal  pupil  contraction. 

Mirror.     An  instrument  of  regular  reflection,  thus  capabk  of  creating  images. 

Motor  Muscles.     The  muscles  that  control  the  movements  of  the  eyes.     The  Recti. 

Mydriasis.     An  abnormal  dilation  of  the  pupil. 

Mydriatic.     A  drug  that  acts  to  dilate  the  pupil. 

Myopia.  An  eye  that  possesses  equal  refraction  in  every  meridian,  but  the  retina  is 
situated  beyond  the  principal  focus  of  the  refracting  system. 

Myotics.     A  drug  that  contracts  the  pupil. 

Near  Point.  The  closest  point  to  the  eye  of  distinct  perception,  usually  measured  by 
Jaeger's  test  type.     Punctum  Proximum. 

Nerve,  Optic.  Tlie  nerve  tliat  transmits  retinal  sensations  to  the  centres  of  percep- 
tion in  the  brain,  there  lo  be  translated  into  sight. 

Neuritis,  Optic.     Inflammation  of  the  optic  nerve. 

Neutralizing.  Destroying  power.  The  term  used  to  designate  the  process  of  deter- 
mining the  power  of  an  unknown  lens. 

Nyctalopia.  Night  vision,  or  day  blindness.  A  term  used  to  describe  an  improve- 
ment in  visual  acuity  in  subdued  light  caused  by  a  dilation  of  the  pupil.  A 
condition  noted  in  Optic  Atrophy  and  Toxic  Amblyopia. 

Nyst.^gmus.  An  involuntary  oscillating  movement  of  the  eyes.  A  condition  fre- 
quent in  albinism. 

Objective  Methods.  Methods  of  estimating  the  refraction  of  an  eye  without  the 
assistance  of  the  patient  by  direct  observations  of  the  operator.  The  most 
important  objective  methods  are  Ophthalmoscopy,  Retinoscopy  and  Ophthal- 
mometry. 

Oblique  Illu.mination.  A  method  of  focusing  light  obliquely  upon  the  cornea. 
Used  in  e.vamination  of  the  cornea  for  opacities,  scars,  etc. ;  also  to  ascertain 
progress  of  cataract  development. 

Ocular  Refraction.  The  science  treating  of  the  optical  conditions  of  the  eye,  the 
estimation  of  its  errors  of  refraction,  and  their  connection  with  lenses  for 
the  eye. 

Opacities.  Obstructions  to  the  passage  of  light  through  the  eye,  usually  located  on 
the  cornea  or  in  the  crystalline  lens.  Cataract  causes  an  opacity  of  the  lens. 
Opacities  of  the  cornea  are  frequently  traceable  to  inflammation. 

Opaque.     Impervious  to  light. 

Ophthalmometer.  An  instrument  for  measuring  the  corneal  curvatures  of  the  eye 
to  locate  corneal  astigmatism. 

Ophthalmoscope.  An  instrument  for  examination  of  the  interior  of  the  eye.  De- 
vised by  Helmholtz. 

Optical  Corrections.  Lenses  that  change  the  direction  of  light  rays  entering  the 
eyes  to  such  direction  as  the  eyes  are  adapted  to  receive  and  focus  them  upon 
the  retina.     Creating  artificially  emmetropic  conditions  when  ametropic  exist. 

Optical  Image.     See  Image. 

Optic  Atrophy.     Partial  or  total  loss  of  sight  due  to  an  impairment  of  the 


GLOSSARY.  197 

Optic  Axis.     An  imaginary  line  drawn  from  the  macula  lutea  through  the  optical 

centre  of  tlie  refracting  system  of  the  eye  to  the  point  of  fixation. 
Optic  Di.sk.     The  head  of  the  optic  nerve  seen  with  the  ophthalmoscope. 
Optic  Nerve.     See  Nerve. 

Optic  Neuritis.     Inflammation  ,,f  the  (iptic  nerve. 
Optometer.     An  instrument  t^  nuMsurc  the  refraction  of  the  eye. 
Orbit.     The  bony  cavity  in  the  skull  that  contains  the  eye. 
Orthophoria.     A  normal  halance  Ijetween  the  motor  muscles. 

Paralla.x.     The  difference  of  direction  of  a  body  as  seen  from  two  different  positions. 
Paralysis.     Loss  of  power  of  motion  in  a  muscle. 
P.\TH0L0Gic.     Pertaining  to  diseased  conditions. 
Penu.mbra.     A  partial  shadow. 
Perception,  Centres  of.     Those  portions  of  the  brain  that  are  the  sources  of  the 

optic  nerves. 
Perimeter.     An  instrument  for  measuring  the  field  of  vision. 
Periphery.     The  edge  of  a  circular  body. 

Periscopic.     a  form  of  lens  having  one  surface  concave,  the  other  convex. 
Phorometer.     An  instrument  for  measuring  the  strength  of  the  recti. 
Photophobia.     Intolerance  to  light. 
PiN-HoLE  Disk.     A  blank  disk  pierced  with  a  small  round  hole,  used  to  determine 

if  sub-normal  acuity  of  vision  is  due  to  an  error  of  refraction. 
Point  of  Fixation.     The  point  to  which  the  look  is  directed. 
Point  of  Reversal.     In  Retinoscopy  the  term  is  used  to  designate  the  point  between 

an  erect  and  an  inverted  image,  where  the  change  from  one  to  the  other  occurs. 

Where  convergent  rays  change  to  divergent  rays.     The  myopic   far-point  in 

Retinoscopy,  where  the  movement  of  the  reflex  appears  choked. 
Presbyopia.     A  physical  change  that  occurs  in  the  eye,  progressing  according  to  age. 

A  loss  of  the  power  of  accommodation. 
Principal  Focus.     The  point  where  parallel  rays  of  light  meet  after  refraction  by  a 

convex  spherical  lens. 
Prism.     An  optical   instrument   of   refraction   having  two   plane  surfaces   inclined 

toward  each  other ;   light  rays  passing  through  a  prism  are  bent  toward  the 

thicker  portion,  called  the  base. 
Prism-Dioptre.     The   unit   of  measure   for  prism  value,   devised   by   Prentice.     A 

prism  that  deviates  a  ray  of  light  one  centimeter  at  one  metre  distance. 
Progressive  My'OPia.     Myopia  with  tendency  to  increase. 
Protractor  Scale.     A  device  for  indicating  the  location  of  the  axis  of  a  cylinder 

lens. 
Ptosis.     Drooping  of  the  upper  eyelid. 
Pterygium.     A  wedge  shape  growth  of  membrane  on  the  conjunctiva,  w'ith  its  point 

toward  the  cornea.     Usually  occurs  with   sailors  and  others  exposed  to  the 

cutting  winds. 
PuNCTUM  Proximum.     See  Near-Point. 
Punctum  Remotum.     See  Far-Point. 

Pupil.     The  circular  opening  in  the  iris  that  admits  light  to  the  eye. 
Radiant  Point.     A  point  from  which  light  diverges. 
Range  of  Accommodation.     The  distance  between  the  near-point  and  far-point  of 

the  eye. 
Reflection   (Bending  backward.)     In  optics,  applied  to  the  change  of  direction  of 

light  rays  incident  upon  a  surface  that  is  not  transparent.     See  Mirror. 
Refracting  Media.     See  Media. 


igs  cular       refraction. 

Refhacting  System.     A  lens,  or  combination  of  lenses,  for  the  creation  of  optical 

images. 
Refraction   (A  bending).     Applied  to  the  change  of  direction  of  light  rays  pass- 
ing from  one  medium  into  another  of  different  density. 
Retina.     The  inner  nervous  coat  of  the  eye  that  is  sensitive  to  light  impulses,  thus 

registering  the  optical  images  formed  upon  it  by  the  refracting  system  of  the 

eye. 
Retinal  Reflex.     A  term  used  in  Retinoscopy  to  designate  the  light  reflected  from 

the  retina  and  creating  the  light  in  the  pupil. 
Retinitis.     Inflammation  of  the  retina. 

Retinoscope.     An  instrument   for  the  practice  of  the  objective  test  called  Retino- 
scopy.    By  its  use  a  beam  of  light  is  directed  into  the  eye  under  observation, 

creating  a  reflection  from  the  retina.     See  Retinoscopy. 
Retinoscopy.     The  name  given  to  the  objective  method  of  estimating  the  refraction 

of  the  eye  by  creating  a  reflex  of  light  from  the  retina.     The  manner  in  which 

these  reflected  rays  emerge  from  the  eye  indicate  its  refraction.     Also  called 

Skiascopy  and  The  Shadow  Test. 
Reversal  Point.     See  Point  of  Reversal. 
Rotation  of  the  Mirror.     A  term  used  in  Retinoscopy  to  indicate  the  movement  of 

the  mirror  to  create  a  movement  of  the  light  area. 
Scissors    Movement.     A   peculiar   movement   of  the   retinal   reflex,    resembling  the 

opening  and  shutting  of  a  pair  of  scissors.     It  ind,icates  a  condition  of  irregular 

astigmatism. 
Sclera.     The  outer  coat  of  the  eye.     The  white  of  the  eye. 
ScLERiTis.     Inflammation  of  the  sclera. 
Scotoma.     A  spot  in  the  visual  field. 
Shadow  Test.     See  Retinoscopy. 
Skiascopy.     See  Retinoscopy. 

Snellen's  Test  Type.     The  standard  for  measuring  and  recording  visual  acuity. 
Spectrum.     The  effect  created  when  white  light  is  separated  into  its  component  colors 

by  a  prism. 
Squint.     See  Strabismus. 
Staphy'LOma.     a   bulging   of  the   ocular   coats;     it   usually   occurs   at   the   weakest 

portion,  the  back  of  the  globe,  and  is  then  called  Posterior  Staphyloma.     A 

common  sequence  of  myopia. 
Stenopaic  Disk.     A  blank  disk  having  a  straight,  narrow  slit,  used  to  locate  the 

principal  meridians  of  an  astigmatic  eye. 
Strabismus.     A  deviation  of  one  eye   from  the  normal  visual  angle.     Convergent 

Strabismus,  an  inward  squint,  frequently  traceable  to  hypermetropia. 
Stye.     A  small  boil  upon  the  eyelid.     Usually  an  evidence  of  eye  strain. 
Subjective  Methods.     Methods  of  estimating  the  refraction  of  the  eye  by  asking  the 

ability  to  recognize  certain  forms  and  test  types. 
Sursumduction.     The  power  required  to  overcome  a  diplopia  created  by  placing  a 

prism  base  down  before  the  right  eye  or  base  up  before  the  left  is  called  Right 

Sursumduction;  base  down  before  the  left  or  base  up  before  the  right  is  Left 

Sursumduction.     A  normal  power  of  sursumduction  is  2  to  3. 
Tenotomy.     The  operation  of  cutting  the  motor  muscles  to  correct  squint  or  relieve 

muscular  imbalance. 
Tension.     The  hardness  of  the  eyeball. 
Test,  Cover.     A  test  for  muscular  imbalance  by  covering  one  eye  and  observing  its 

movement  when  uncovered;  the  point  of  llxation  being  established. 


O  S  S  A  R   Y. 


199 


Toxic  Amblyopia.     Amblyopia  caused  by  a  poison,  a  common  cause  being  excessive 

use  of  tobacco  or  liquor  or  both. 
Transit.     A  passing  across.     A  term  used  in  Retinoscopy  to  indicate  movement  of 

the  light  area. 
Translucent.     A   condition   between  transparent  and  opaque.     Permitting  partial 

transmission  of  light. 
Transparent.     Having  the  property  of  permitting  rays  of  light  to  pass  through,  so 

that  objects  may  be  seen  through  a  transparent  object. 
Transposition.     In  optics  a  change  of  form  without  altering  the  optical  value. 
Tunics.     The  ocular  coats. 
Umbra.     A  shadow. 

Visual  Acuity.     The  measure  of  sensibility  of  the  eye  and  the  power  of  perception. 
Vitreous.     The  jelly-like  humor  of  the  eye. 
Working  Distance  in  Retinoscopy.     The  distance  of  the  operator  from  the  eye 

under  observation  when  the  reversal  point  is  located. 
Yellow  Spot.     See  Macula  Lutea. 


The  Key  to 
Optic  JvlKnov 


The  Optical  Journal 

PubliBh.d  the  lat  of  es    ' 
month.     160  pagea. 

$2  year.  joc.  a  copy. 

Eighth  year  of  success. 
36  MaldOB  Lue,  New  Yori. 


INDEX    OF      SUBJECTS 


Aberration. 

Clininialic    S3 

Sl'lH-ru-al    44 

Acc.ininiiMhilii.n 109 

Range  of  in 

Achromatic  Refracting  Systems....  9.2 

Acnity  of  Vision 118 

.Albinos    105 

.Allowance   for   Working  Distance. 

.181,  182 

Ametropia  127 

.\niplituclc  of  Accommodation m 

Anglo   of    Incidoni-e i  ? 

Critical    M 

Of    Reflection 14 

Of  Vision I TQ 

Anisometropia   141 

.Aperture  of  a  Mirror 17 

Formation  of  Image  liy  an 21 

Appearance    of    the    Retinal    Reflex, 

175.  176 

Aqueous  Humor  104 

Area   of  Light  on   the    h'ace 171 

And   Shadow  in   the   Pupil.  .17J,   176 

On  the  Retina 172 

Assymmetrical   .Axes   130 

Asthenopia    142 

Astigmatism  of  a  Lens 66 

Against  the  Rule 139 

Assymmetrical  139 

At  Oblique  Axes 185 

By  Incidence   98 

Locating  the  Axis  of,  with  the 

Retinoscope   173 

Of  the   Eye 135 

The   Light    Band    Characteristic 

of    T--; 

With  the  Rule 139 

Astigmatic    Test   Charts 07 

Axis,  Principal,  of  a  Alirror 17 

Locating  the   Axis   of    Correct 
ing  Cylinder  for  .Astigmatism 

with   the   Retinoscope 173 

Principal,  of  a  Lens 30 


Secondary,  of  a  Mir'or 39 

Secondary,  of  a  Lens 18 

Band  of  Light  Cliaracteristic  of  As 

tigmatisni 173 

Beam   of   Liyht 9 

I'.iii.icular   X'lsion I16 

i'.liii.l    Si". I    .if  the   Eye loi 

r.iilliaiiCN    ..f    Retinal    Reflex,    Com- 

paralu'c    180 

Camera   98 

Centre,   Optical    46 

Geometrical    46 

Of  Curvature  17 

(VnliT.I   l.ni.   49 

Conlral    .\rtrrv    104 

Ch..ke(l   .\|i]iearance  of  the  Reflex..  176 

Choroid loi 

Chromatic  .\berration   53 

Ciliary  Muscle   103 

Processes    103 

Circle   of   Diffusion 96 

Color    13 

Blindness i  if^ 

Spectrum  5,^ 

Compound  Lenses   68 

Generic  and  Contra-Generic...  68 

Concave  Spherical  Lens 51 

Rec.'.£;iiiti..ii    ..t 53 

Virtual    1".,<M.   ..f 51 

Concavv    Miri.T      17 

Inia-<-    ("r.ai.-.l    l.v    a 19 

Its    .Xiirrmrr..,' 17 

It-.  Wri.v    17 

Its    I'rnini.al    .\xis 17 

It-^    I'nnnpil    I .  ,ru. 18 

Conju'^a'i.''     !■'..>',     uuh   'a'    Concave 

:\Iirror    'O 

Of   the    Eve LSO 

Positive    '59 

Virtual    159 

With  a  Convex  Lens 41 

Conjunctiva  I03 

Convex  Spherical  Lens 39 

Formation  of  Image  by  a 41 

_      Recognition  of ■  ■  49 


20> 


OCULAR 


K   F   R   A   C  T   I  ON. 


Convex  Mirror   20 

Image  Created  by  a 20 

Optical   Effects  of  a 20 

Contra-Generic  Compound  Lenses . .  &S 

Convergence    117 

Cornea   loi 

Critical  Angle 34 

Crystalline    Lens loi 

Cycloplesjic.   I'sc  nf  in  Retinoscopy.  166 

Cylinder    l.rn^ 60 

Am.     it    60 

Char,,,-,,.,-,-,,,-.   ,„   a 83 

Prill,-, |i,il     \l,-,-i,li;in    ,-.f 61 

Pris,,,    C.iMlnii,-,!    With ,S4 

Rcf,-;,,-,.,.,,    In     :i 62 

SplH-nc.il    (  ,.nil,iii,-,l    Wilh 6q 

To  Locate  the  Axis  of  a 82 

Decentration  of  a  Lens 86 

Decentred   Lens 50 

Determination     of     Refraction     by 

Retinal  Reflex 178 

Diffused    Light 26 

Dioptre   56 

Dioptric   System 56 

Dispersion   of   Light 53 

Disk,    Stenopaic 65 

Pin-hole    65 

Dominant    Eye 141 

Donder's    Rule 140 

Drops  in  the  Eye 167 

Emmetropia    122 

Emmetropic    Eye 109 

Energy,    Radiant 5 

Errors  of  Refraction 122 

Estimation     of     Myopic     Far-point 

Without  a   Lens 182 

Ether  7 

Exai-nples  in  Transposition 72  to  80 

External    Recti 105 

Eye,   Accotnmodation  of 109 

Ametropic    127 

Aqueous    Humor 104 

Astigmatic   135 

F>lind   Spot  of lor 

Central  Artery  of 104 

Ciliary  Muscle  of 103 

Ciliary   Processes   of 103 

Conjunctiva    of 103 

Cornea    of loi 

Crystalline  Lens  of loi 

Dominant    141 

Drops   in  the 167 


Emmetropic    

Exannnation     of 

External  Recti  of 

l''ar-point  of 

Humors   of 

Hypermetropic    .• 

Iris  of 

Internal   Recti   of 

Inferior  Oblique  Rectus  of. 

Inferior  Recti 

Macula-lutea  of 

Membranes  of 

Model  

Motor    .Muscles 

Myopic  

Normal    

Near-point   of 

Optic   Foramen   of 

Pupil    of 


Aci 


of. 


^^-Il,1^v    Si.,,1   ..f 

EvclicN   

Far-point  of  the  Eye 

Field    of   Vision 

Fixation  

Focal  Length  of  a  Mirror 

Of   a   Lens 

Focus.   Principal 

Of  a  ?^Iirror 

Of  a  Lens 

Geometrical    Centre 

Generic  Compound  Lenses 

Helmholtz,   Extracts    Im-ohi   F"a, 


As  Indicated  by  the  Retinoscope. 

Correction  for 

Identical  Points  on  the  Retina 

Illuminated    Bodies 

Image,   Optical 

Formation  of  by  an  Aperture.  . . 


N  D  E  X 


O  F 


Formation  of  by  a  Plane  Mirror.     22 
Formation     of    by     a     Concave 

Mirror    23,     2$ 

Formation     of     by     a     Convex 

Mirror    25 

Forination     of     by     a     Convex 

Spherical  Lens 41,     43 

Inversion  of  by  a  Mirror 15 

Real   20,     41 

Virtnal  20,     43 

Inch  System  of  Numbering  Lenses.  .     54 

Incident    Rays 13 

ln<l.-x   of   RrfraclM.n 34 

liilVn.ir    krrii 105 

<  )lili.|iu-    Keclus 105 

Internal    Recti 104 

Ins    103 

Lachrymal   Organs lOI 

Lens,    Centred 49 

Concave   Spherical 51 

Convex   Spherical 49 

Componnd 68 

Decentred    So 

Definitions  of 39,     40 

Periscopic   46,     58 

Principal  Axis  of 39 

Principal  Focus  of 39 

Second.irv  .\\i^  nf 39 

Toric   69 

Light    7 

Absorpiioii  ..1 12 

And  Sliaduw  in  the  Pnpil...i72,  176 

Area  on  the  bace 171 

Area  on  the  Retina 172 

As  a  Form  of  Fnergy 7 

Band  of.  Typical  of  Astigmatism.    173 

Beam  of 0 

Diffusion  of 26 

Direction  of 8 

Dispersion  of 53 

Intensity  of 11 

Invisibility  of 8 

Pencil- of •. to 

Radiation  of 11 

Ray  of 9 

Reflection  of 13 

Refraction  of 27 

Refrangibility  of 53 

Transmitted 12 

Velocity  of 6 

Locating  Myopic  F'ar-point  Withont 


SUBJECTS.  203 

,        .   ''    I-^'ii-' 182 

^"'t;;;;^ '='■■'- - 

.Membrane.  ,,f. he   l^ve ,0, 

Meth.Ml,    Ol.jeenve ,46 

Of  LocatmgMycp.c  Far-point..  182 

Subjective   146 

Microscope   4^ 

-Mirror    '  '  '  {^ 

Aperture  of  a [  17 

Centre  of  Curvature  oi.  . .'.'.'..'.  17 

g;;;;-- '' 

\j'"^^^ 20 

Focal  Length  of 18 

Plane    ,5 

Principal  Axis  of 17 

Principal  Focus  of 18 

Secondary    Axis    ,,\ ig 

Tilting  OI-   K. .latin-    ihe '..'.    169 

Model    Eye   for    I'raetKe   ,,f   Rctino- 

scopy 165 

Motor    Muscles 104 

Movement,    Scissors 189 

Movement  of  the  Light  Area 171 

Retinal    Reflex 176,  178 

Muscles,    Motor 104 

Ciliary  103 

Myopia    132 

.As  Indicated  by  the  Retinoscope.   179 

Correction   for 1^5 

Near-point   of  the   Eye I'i'i 

Neutralizing    Lenses'. ,S8 

Normal    Eye 107 

Objective   IMethods 146 

Examination    147 

Ophthalmoscope    147 

Optical,    Images 20,     92 

Centre    46 

Neutralizing    88 

Prisms    ^-^y 

I  o    Locate 46 

Optics,    Physical gr 

Physiological    91 

Optic    Nerve loi 

Foramen    1 04 

Orbits  of  the  Eye 101 

Orthophoria    117 

Pencil    of    Light 10 

Periscopic   Lenses 46,     58 


204 


OCULAR         REFRACTION 


Physiology  and  Anatomy 

Pin-hole    Disk 

Piano   Glass 

Curved    

Position  of  Patient  and  Operator.  .. 

Primary  of  Light  Area 

Secondary  of  Light  Area 

Practice,  Value  of  in  Retinoscopy.  . 

Of  Retinoscopy  With  jNIodel 
Eye   i6s, 

Of    Retinoscopy    Illustrated    by 

Diagrams  i6i,  162, 

Presbyopia    

Principal   Focus 18, 

Axis    17, 

Meridians    ,.61, 

Protractor    Scale 

Prism   

Optical  Effects  of 

Punctuni   Proximum 

Remotum    

Pupil    

Radiant    Energy 

Range  of  Accommodation 

Rate  of  Movement  of  Retinal  Reflex. 
Ray  of  Light 

Emergent    

Incident    

Reflected    

Real    Image 

Recti   • 

Reflected    Ray 

Reflection    

Angle  of   

By  Plane  Mirror 

By   Concave    Mirror 

By   Convex   Mirror 

Inversion  by   

Multiple  

Total   

Refraction    

By   Plane   Glass 

Cause  of  

Errors  of 

How  It  Occurs 

Index   of 

Total   

Refracted  Ray 

Refracting   Systems 

Achromatic    

Media  of  the  Eye 


Ref rangibility   of   Light 53 

Retina     loi 

Retinal  Reflex 172 

Comparative  Brilliancy  of 180 

^Movement  of 176,  179 

Rate  of  Movement  of 180 

Retinoscope   148 

Concave    Mirror 145 

Control   of 168 

Luminous    161 

Method  of  Holding  the i6g 

Method  of  Operating  the 170 

Plane    JMirror 145 

Retinoscopy    14S 

Allowance     for     Working    Dis- 
tance in 181,  182 

Its   Theory    Explained    by    Dia- 
grams    161,  162,  i6j 

Rule    for    Transposing    Inches    Into 
Dioptres    and    Dioptres    Into 

Inches    56 

Rules    for    Transposition    of    Com- 
pound Lenses 76  to  79 

Donder's    140 

For  Decentration  of  Lenses....     86 

Scissors    Movement 186 

Sclerotic    loi 

Secondary  Axis  of  a  Mirror 18 

Of   a   Lense 39 

Position  of  the  Light   Area 176 

Sliadow    Test 176 

In  the  Pupillary  Area 173 


Sight 

Snellen's   Test   Types. 

Spectrum   

Si.Iini,,,!    L,  n-,  , 


6 
119 

53 
39 

Sl.li--.'.'      \I..M.iiH.n 44 

Spli.  I..  I   -    ■    .'.  ■    Lenses 69 

Slcn^-lMu-    1'-^-. 65 

StcreoNCiipic    Pictures 99 

Subjective  Methods 146 

Superior  Recti 105 

Oblique   Rectus 105 

System  of  Recording  Axis  of  Cylin- 
drical Lenses 68 

Table  of  Dioptric  and  Inch  Systems.    57 

Tears    loi 

Test    Charts,  Astigmatic 97 

Types,    Snellen's 119 

Theory  of  Light 7 

Of    Retinoscopy    Explained    by 


INDEX        OF 

Diagrams    i6i   10163 

Of  Working  Distance  in  Retino- 
scopy  Explained  by  Analogy.   163 

Theorems  for  Transposition 71,     72 

Toric   Lenses 68 

Total    Reflection 34 

Transit  of  the  Pupil 171,  176 

Of  the  Light  in  Astigmatism..   185 
Of  the  Light  in  Spherical  Ame- 
tropia        183 

Translucent   Bodies 12 

Transparent    Bodies 12 

Transmitted    Ray 12 

Transmission  of  Light 12 

Transposition    71 

Of  Inches  Into  Dioptres 56 

Of  Dioptres  Into  Inches 56 

Rules  for 76  to  79 


SUBJECTS.  205 

Use  of  a  Cycloplegic 166 

Velocity  of  Light 6 

Vertex   of    Mirror 17 

Virtual    Image 20,  43 

Focus     24 

Vision,  Binocular 116 

Field    of Ii6 

Line  of 116 

Single  116 

Visual    Acuity 118 

iNIeasuring    119 

Recording   119 

Visual    Angle iig 

Vitreous   Humor 104 

Wave  Theory  of  Light 7 

Working  Distance  in  Retinoscopy. .  159 

Allowance   for 181,  182 

Yellow    Spot loi 


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